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# Math 54 Berkeley Notes

	Para- metric equations and polar coordinates. The material covered in this course is extremely important both because it is applied in a variety of disciplines (actually, it is quite hard to come up with an area where it cannot be used) and because it develops concepts that form the basis of many areas of modern. A deficient grade in Math N10A may be removed by completing Math 10A. Discrete Math and its Applications, 7e, Kenneth E. Monster Primes; Mathemagic; Kelly's Math Salad; Math Resources. Find MATH study guides, notes, and practice tests for UC Berkeley. The TAs will spend very little time reviewing material that is not specific to. Students are strongly encouraged to conduct research during their junior/senior years, particularly if interested in continuing to a graduate program. Some volumes are "works in progress" that are intended for a more complete treatment in later publications. Text: Boyce and DiPrima. Introduction to Analysis Department of Mathematics University of California, Berkeley Spring 2009 This is an introductory course on analysis. , Pauley Ballroom  Make sure you revisit the notes after. The guy absolutely lives math, yes lives. He develops the mathematics first using electromagnetism (i. 2 hen-1) that was typical of industry practice. Welcome to Math 54! This fantastic course is an introduction to linear algebra and its applications to differential equations. UC Berkeley requires additional lower division courses for graduation beyond those listed or articulated. 	4% state average. Click to share on Facebook (Opens in new window) Click to share on Twitter (Opens in new window) Click to email this to a friend (Opens in new window) Click to print (Opens in new window) Packed. That’s one major take-away from the 2019. UCSD Math 20D Differential Equations old exams from Ed Bender and also Math 21D from Bruce Driver. Our services seek to foster a student-centered environment that allows students to thrive and succeed while engaging with the mathematics and statistics they encounter throughout the UC Berkeley undergraduate curriculum. because I plan on taking 1B if I end up attending Berkeley. Taking more than one of Math 53, 54, or 55 helps somewhat, but many students do well without this. The TAs will spend very little time reviewing material that is not specific to. George Berkeley (/ ˈ b ɑːr k l i /; 12 March 1685 - 14 January 1753) - known as Bishop Berkeley (Bishop of Cloyne) - was an Irish philosopher whose primary achievement was the advancement of a theory he called "immaterialism" (later referred to as "subjective idealism" by others). It’s no surprise if you need a little extra help in either class. The graph Laplacian and Morse inequalities , with B. As a 54-year-old black woman, she also offers a compelling profile for Democrats hungry for diversity and fresh faces. The Superquiz that never happened. shigeru-histsci. I think I'll be okay with my two breadth classes (can take one of them p/np but not the other) but since I got a C- in Math 1B and a B in 61A I need to get good grades in the rest of the CS prereqs. 		; Genus Integration, Abelianization and Extended Monodromy, with R. For the third problem, let T = 0 correspond to time of discovery, not time of death. Each note may be covered in one or more lectures. Some of the test banks may include answer keys as well. Students at Berkeley Vale Public School are confident, creative, active informed citizens. Berkeley Math Circle, San Jose Math Circle. However, units earned for these approved substitutions are non-business upper division units and students must take additional business electives towards the required 38 upper division business. Low-Frequency Earthquakes (LFEs) are commonly used to identify when and where slow slip occurred, especially for slow slip events that are too small to be observed geodetically. Indeed, though this approach is by design popular with white voters, it holds even greater. Some previous Math 54 exams: Math department archive Tau Beta Pi archive Math 54 Worksheets. Math department list of tutors. The material covered in the course does not correspond to a university level mathematics course offered at the University of Michigan. At UC Berkeley I received my PhD under the supervision of Denis Auroux. The Berkeley Math Circle. JMP and JMP Pro are used in the statistics/mathematics fields and in any research, administration or field of study in which interpretation of statistics is necessary. Note: If you are a double major with physics, then the maximum number of classes above that can count as electives for Astro is 2 (you can cross-list two classes across the two majors). Speak to the professor about what strategies you should use to prepare for the final, they'll often drop hints. However, as is often the case with related rates/implicit differentiation problems we don't write the $$\left( t \right)$$ part just try to remember this in our heads as we proceed with the problem. Instructor: Katrin Wehrheim Office: Evans 907 Email is not a sustainable form of communication in this. Study University of California - Berkeley Mathematics 54 flashcards and notes. 	For example, convert centimeters to meters, convert kilograms to grams. Certain sections will prioritize certain groups of students (e. This is a combination of two textbooks specifically for this course. Linear Algebra and Differential Equations, Second Custom Edition for UC Berkeley, by Lay, Nagle, Saff and Snider. Tips to succeeding in Math 54?  Note that the proof based questions in the book are significantly harder than the ones on the exam, so if you are able to get like. Sixth Grade - Table of Contents. com reports. Outside of mathematics my hobbies include playing piano, salsa dancing, board games, and cooking things in large pots. s in Economics. besides me i don't know any other guys doing it. The notes have been only minimally edited, and there may be several errors and imprecisions. Which to self study over summer: Math 54 or CS61B? I'm taking a somewhat difficult courseload (IMO) in the fall. Math 54; Math 54. Find MATH study guides, notes, and practice tests for UC Berkeley. Peyam Tabrizian's Math 54 web page. If you have taken only the diﬀerential equations part of this course, solve only problems. Math department list of tutors. x 2 +1 > 0. 		Monogram "V. If you have completed any of the math prerequisites at a non-UC institution, please look at Frequently Asked Questions. Math 1A Fall 2015 Professor Coward This blog is to keep students updated on what happens in Professor Coward's Math 1A Lecture this semester. Students planning to enroll in Data 100 should plan to complete the required co-requisite, Math 54 or EECS 16A. I can be reached at [email protected] These textbooks are. Note: CS 70 is a required pre-req for several of the CS and Math electives in the senior year;  [email protected] This page contains sites relating to Discrete Math. There is typically very limited space in the class, I think we had about 20-25 for a full size Math 54 class. This document is an attempt to provide a summary of the mathematical background needed for an introductory class in machine learning, which at UC Berkeley is known as CS 189/289A. com, the largest library of official, licensed digital sheet music. Aubrey Clayton, [email protected] The Adjunct courses explore key study and test-taking strategies, and problem solving techniques specific to the lecture they are linked to. Berkeley Mathematics Lecture Notes This series makes available at low cost several collections of notes from graduate and undergraduate mathematics courses taught at the University of California at Berkeley. Economics All applicants are expected to have completed intermediate math-based economic theory courses. Discover the best homework help resource for MATH at University of California, Berkeley. 	John William Lott (born January 12, 1959) is a Professor of Mathematics at the University of California, Berkeley. The notes have been only minimally edited, and there may be several errors and imprecisions. that the class is taken alongside Math 53, 54, or 55. The position listed below is not with Rapid Interviews but with Department of the Navy Our goal is to connect you with supportive resources in order to attain your dream career. However, his material is hard. Each section has solvers (calculators), lessons, and a place where you can submit your problem to our free math tutors. These textbooks are. Berkeley Math Circle: Monthly Contest 7 Solutions 1. Prerequisite Areas Course Options General Psychology One of the following is required:. one of the main math people at berkeley, and he says that he is a math genius, and still had to put. These textbooks are. Notes * A minimum of 120 units is required for graduation. pdf from MATH 54 at University of California, Berkeley. Here is my CV (pdf, updated August 2018). I was doing perfect in hws and pretty good on quizes. 		If you have taken only the linear algebra part of this course, solve only problems 1, 2, 3 (labeled LA). The last day to complete a bSpace Content Retrieval Request was Friday, June 16, 2017. contact mail: 530 Evans Hall. Math 53 and 54 get very fast/tricky at the end of the semester. Bon-Soon is a legend. Sahai, from Fall 2014: Notes on Chernoff Bounds And here are some additional notes compiled by previous TAs: Sinho's notes on CS70 ; Alvin's notes on CS70. Rosen, McGraw-Hill, Inc. Discrete Mathematics and Probability Theory. Blackwell also displayed a natural ability to locate loose balls and clog passing lanes, racking up nine steals in the dominant win. I can only compare the undergraduate math here to a few private universities since those are the only ones I know anything about, and my response is more aimed towards people who have dabbled in a bit of math in high school, but here goes (if you'. In this series, we will try to understand the underlying mechanisms and concepts of the black box that Deep Learning. Welcome to the Berkeley Parents Network! Berkeley Parents Network (BPN) is a nonprofit network for parents who live in the San Francisco Bay Area. Math Web form, or browse the extensive archive of previous questions and answers. Some of the test banks may include answer keys as well. 090909 Only fractions in lowest terms are listed. Discover the best homework help resource for MATH at University of California, Berkeley. Grading and policies. 	The Berkeley Math Circle. Check regularly for updates. Use margins for questions, comments, notes to yourself on unclear material, etc. WebMath is designed to help you solve your math problems. Also, the rst chapter is sketchy and unreadable. UPD Samplexes provides sample exams or samplexes, readings, photocopies, reviews about teachers, and materials to students of UP Diliman for free. learning, which at UC Berkeley is known as CS 189/289A. and 54 Degrees, While Applying Both to Geometry Problems" (Intermediate)  (Note: Expanded handout. Also see exams from Math 123. 06/21/2011: Finally finished with the lecture notes! I added Lectures 25 and 26, so these lecture notes are now complete, if not completely correct. Number Theory Combinatorics Geometry Algebra Calculus & Diff Eqs Probability & Statistics Set Theory & Foundations: Reflections on Relativity History Physics. Pre-Algebra, Algebra I, Algebra II, Geometry: homework help by free math tutors, solvers, lessons. Students at Berkeley Vale Public School are confident, creative, active informed citizens. Some previous Math 54 exams: Math department archive Tau Beta Pi archive Math 54 Worksheets. Bon-Soon is a legend. In terms of mathematics, your algebra should be very solid, you need to know basic probability, and you should be comfortable with thinking abstractly. on bcourses. ] Fixed typo in project 3. Academic honesty. 		because I plan on taking 1B if I end up attending Berkeley. The guy absolutely lives math, yes lives. Mathematically, my interests lie in symplectic, algebraic and tropical geometry, specifically mirror symmetry. Before going to class, some students have found it helpful to print out Purplemath's math lesson for that day's topic. Note 24: The Chinese Remainder Theorem and Remote Coin Flipping; Extra Notes Here are some additional notes on Chernoff Bounds by Prof. Long Monotone Paths in Abstract Polytopes, with R. Math 54: Linear algebra and differential equations | MATH 54 002: Linear Algebra and Differential Equations is a course taught at University of California, Berkeley (UC Berkeley) by. MATH 1A & MATH 1B Calculus MATH 54 Linear Algebra and Differential Equations. ly This is where most of Berkeley's confessions are - on the "Confessions & Rants" page, at least. Introduction Although several writers, for example Bernisteini, Levy, and Ville, had used whatwouldnowbeidentified as martingaleconcepts, thefirst systematicstudies. Call Type: EPA CONTRACT SPT Minimum - \$619/wk. Introduction to Analysis Department of Mathematics University of California, Berkeley Spring 2009 This is an introductory course on analysis. 090909 Only fractions in lowest terms are listed. This content is password protected. Math department list of tutors. Welcome! This is one of over 2,200 courses on OCW. 	In order to ease the transition, we plan to focus on more of the abstract concepts found in calculus, linear. Prerequisite Areas Course Options General Psychology One of the following is required:. During my senior year of high school I took a Differential Equations class and it covered almost everything that the Math 54 course covers. Math 110 (Linear Algebra) Lots of computer science students are interested in taking this course because they hear that it is the "true" linear algebra course, unlike math 54. This below is a picture of Evans hall. MATH 1A & MATH 1B Calculus MATH 54 Linear Algebra and Differential Equations. Join us for this special event that celebrates music, culture and dance by young Australian talent. Math 54 ﬁnal, Spring 2010, John Lott This is a closed everything exam, except for a 3x5 card with notes. 00 price target on the biotechnology company’s stock. Prerequisites: Math 53 and 54, basic programming skills, Math 104 and 110 a plus. Preparation plan and prerequisites. Presented by the Clay Mathematics Institute, the award notes his “landmark contributions” that include a proof of the global Gan-Gross-Prasad conjecture for a wide class of automorphic representations of unitary groups, a proof he did with Zhiwei Yun of a higher-order generalization of the Gross-Zagier formula over function fields, and a. The inequality : x 4. Additionally, the drivers have been given pseudonyms to protect their privacy. You will be able to declare Computer Science as your major when you complete your remaining technical prerequisites with a Berkeley grade point average of at least 3. **A fifth semester is granted to transfer student admits who are missing at least three lower division technical courses, of at least 3 units each, for the Engineering Mathematics & Statistics major when they matriculate to UC Berkeley. 		The competition will not take place on April 15 & 16 as originally announced. My first midterm was pretty good too (57/60). US employers added 128,000 jobs in October, the Bureau of Labor Statistics said in its monthly jobs report. DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA, BERKELEY Probability theory H. While completely optional, Math 104 is a great place to practice this in writing your homework. Download this MATH 54 study guide to get exam ready in less time!  Berkeley (5,000) MATH (900  sept20 math 54 discussion section. The information in this guide is based on 2015-16 articulation and is subject to change. A deficient grade in Math N10A may be removed by completing Math 10A. Math W53 - Multivariable Calculus (4 units): The purpose of this course is to introduce the basic notions of multivariable calculus which are needed in mathematics, science, and engineering. Berkeley time shows a better grade distribution for Lin Lin but I’ve heard mixed. Preparation in Math and Statistics (Equivalent Berkeley course in parentheses). Lecture Notes for Introductory Probability Janko Gravner Mathematics Department University of California Davis, CA 95616 [email protected] In terms of mathematics, your algebra should be very solid, you need to know basic probability, and you should be comfortable with thinking abstractly. If non-UC Berkeley college level course work was completed before admission into UC Berkeley, it can be used to satisfy. NASA Astrophysics Data System (ADS) Chestler, S. Kent Nagle and a great selection of similar New, Used and Collectible Books available now at great prices. Download, print and play sheet music from Musicnotes. 	Math 53 and 54 get very fast/tricky at the end of the semester. Ulkucu, UC Berkeley OR Center, ORC 75-10, Pages: 1-18, (1975). Nia is a fun, creative, mindful movement technique – a fusion of dance, martial arts and healing movement such as yoga. * Students who do not complete a Math 54 equivalent before transferring are required to complete Phys 89:"Introduction to Mathematical Physics" at Berkeley. com: Linear Algebra & Differential Equations Second Custom Edition for University of California, Berkeley (Math 54 - 2013) (9781256873211) by David C. We partner with leading organizations such as the Academic Internship Council and EUSA to provide you with internship programs and comprehensive support, including: • One-on-one program advising • Placement in an internship based on your academic. Taken from the abstract of notes. Access study documents, get answers to your study questions, and connect with real tutors for MATH math 53 at University Of California, Berkeley. 23 x 10-4 = 0. scienceblog. Text: Boyce and DiPrima. besides me i don't know any other guys doing it. Find all possible values for the nal number left on the board. They have the capacity to communicate effectively and respectfully, and have the values to be responsible, resilient and empathic citizens in our society. Prerequisites Math 1B or equivalent materials. Math 54 had a slightly greater impact than the others (see the statistical study for details). Math 53 introduces (the real point of the class) stoke's and divergence theorem in the last 2 weeks. 8 against the winner of Friday’s Military Magnet-Charleston Math and Science game. There will be no makeup exams, so please do not plan to travel on these dates. AAA Math features a comprehensive set of thousands of interactive arithmetic lessons. 		To view it please enter your password below: Password:. Learn vocabulary, terms, and more with flashcards, games, and other study tools. In Fall 2018, my office hours are 12-2 pm on Wednesday in MCS 227. Students are strongly encouraged to conduct research during their junior/senior years, particularly if interested in continuing to a graduate program. And those classes have silly curves. Math 1B vs Jumping to Math 54. that the class is taken alongside Math 53, 54, or 55. University University of California, Berkeley. The History and Philosophy of Logic, Mathematics, and Science (HPLMS) working group is a forum for the discussion of issues at the intersection of mathematics, philosophy, intellectual history, and science. Tau Beta Pi Engineering Honor Society, California Alpha Chapter. Taken from the abstract of notes. Each minute, two numbers are erased and their sum is written instead. I was planning on taking Math 53, just because it looked like it was before Math 54. A maximum of two approved upper division courses (including the macro and micro theory courses) may be taken outside the department towards upper division major requirements. Founded in 1868 on the San Francisco Bay, UC Berkeley is the flagship campus of the University of California and one of the world's most prestigious public universities. Rajasthan Board Class 8 Mathematics Question Paper – AglaSem Schools 24-Apr-2018 · Here we are providing the Rajasthan Board Prarambhik Shiksha Purnata Praman Patra Pariksha ( Class 8). 	, New York, 2003) is recommended but not required. MATH 54 Linear Algebra and (4)|MATH 24 Elementary (4)  preceding fall enrollment at Berkeley. Transfer students who have not completed Math 54 prior to their first semester at UCB are required to complete Physics 89. Conquer your course and sign up for free today!. Bird * Bind * Wind * Wine * Wise * Wish * Fish Cantor's First Page Kepler's Orbs. You need to justify every one of your answers. I disagree. The Adjunct courses explore key study and test-taking strategies, and problem solving techniques specific to the lecture they are linked to. Eligible transfer students must contact their ESS Adviser in order to request the fifth semester. , New York, 2003) is recommended. 3 girls in my section are doing 53/54 together. Economics All applicants are expected to have completed intermediate math-based economic theory courses. Library 101 Video Watch this short video to learn how to get the most out of the UC Berkeley Libraries and their vast resources. Note that while Nyquist is appropriate for sampling, it may not capture nuances in information. The material covered in the course does not correspond to a university level mathematics course offered at the University of Michigan. Note: If you are a double major with physics, then the maximum number of classes above that can count as electives for Astro is 2 (you can cross-list two classes across the two majors). 		There will be no makeup exams, so please do not plan to travel on these dates. Note: Repeat test takers may take the CAHSEE multiple times in a school year. Math 1B vs Jumping to Math 54. Hi, I am going to take MATH 54 this summer and I am trying to find the free pdf files on the internet. He is by far the best. 090909 Only fractions in lowest terms are listed. Tau Beta Pi Engineering Honor Society, California Alpha Chapter. Sinho Chewi's Website. Berkeley Mathematics Lecture Notes This series makes available at low cost several collections of notes from graduate and undergraduate mathematics courses taught at the University of California at Berkeley. shigeru-histsci. Therefore, students who are planning a double major or a minor with Astrophysics and Physics are required to complete Physics 89 in lieu of Math 54. Hyperbolic manifolds, discrete groups and ergodic theory Math 277 - Fall 1996 - C. Notes • Mizzou's 121 points were the most in an exhibition game during the Robin Pingeton era. But I got very stressed out last night, couldn't sleep a bit and did unbelievably stupid mistakes. Peer Advisors complement the Data Science Advising services by sharing their diverse knowledge of and experiences with major courses, different Data Science Major domain emphases, extracurriculars and student groups on campus, research opportunities, and various campus resources. Math 54 had a slightly greater impact than the others (see the statistical study for details). I think I'll be okay with my two breadth classes (can take one of them p/np but not the other) but since I got a C- in Math 1B and a B in 61A I need to get good grades in the rest of the CS prereqs. Rajasthan Board Class 8 Mathematics Question Paper – AglaSem Schools 24-Apr-2018 · Here we are providing the Rajasthan Board Prarambhik Shiksha Purnata Praman Patra Pariksha ( Class 8). An introduction to stochastic differential equations. 	NASA Astrophysics Data System (ADS) Chestler, S. Graph Theory: Penn State Math 485 Lecture Notes Version 1. DEGREE CHECK – ENGINEERING MATH AND STATISTICS Lower Division Requirements Course Units Grade Note Math 1A 4 1B 4 53 4 54 4 185 Physics 7A 4 7B 4 Math/Stat Technical Electives* 7C 4 Chemistry 1A/1AL or 4A 4 Computer Sciences Engin 7 or CS 61A 4 Engin 177 or CS 61B or 61BL 3-4. Math 54 does the same with Fourier transforms and PDEs. It is highly recommended that you attend both discussions each week. edu June 9, 2011 These notes were started in January 2009 with help from Christopher Ng, a student in Math 135A and 135B classes at UC Davis, who typeset the notes he took during my lectures. Combinations When we want to find the number of combinations of size 2 without repeated letters that can be made from the three letters in the word CAT, order doesn't matter; AT is the same as TA. You should self-study that material before the second half of Math 54, which picks up differential equations from where Math 1B left off. Prerequisites: Math 53 and 54, basic programming skills, Math 104 and 110 a plus. pdf from MATH 54 at University of California, Berkeley. Enrollments For basic enrollment information, please visit the course page in the mathematics department website. 54 alone would be manageable. While there are a number of credit cards currently offering 100,000 point welcome bonuses, not every point is worth the same amount. All the GSIs know what is going on. If you have completed any of the math prerequisites at a non-UC institution, please look at Frequently Asked Questions. From expeditions to Egypt in the late 1800s to stem cell research and artificial intelligence today, Berkeley has been at the forefront of research throughout its history. 		George Bernard Dantzig (/ ˈ d æ n t s ɪ ɡ /; November 8, 1914 – May 13, 2005) was an American mathematical scientist who made contributions to industrial engineering, operations research, computer science, economics, and statistics. Fun: Confess. I believe they labeled it as Math 98 - Adjunct (like most other supplemental classes). Math 1B vs Jumping to Math 54. You may attend any discussion section, but we recommend that you settle on a weekly two-section pair (with the same TA) as early as possible in the semester. org) and Berkeley Scholars web hosting services have been retired as of January 5th, 2018. Peyam Tabrizian's Math 54 web page. Math 53 introduces (the real point of the class) stoke's and divergence theorem in the last 2 weeks. com reports. But I got very stressed out last night, couldn't sleep a bit and did unbelievably stupid mistakes. I will probably get around 40/60 which will be C/C+/B- depending on curve. Tips to succeeding in Math 54?  Note that the proof based questions in the book are significantly harder than the ones on the exam, so if you are able to get like. Math 54 does the same with Fourier transforms and PDEs. Aubrey Clayton, [email protected] Fourier series and partial differential equations. In each experiment, a total of 216 laying hens were used, with 54 hens housed in each of the four calorimeters at the cage stocking density of 435 cm2 hen-1 (67 in. Note 0 is background material that you should make sure you understand before the first lecture. Generous support from the James M. My advisor is Philippe Rigollet. Math 1A Fall 2015 Professor Coward This blog is to keep students updated on what happens in Professor Coward's Math 1A Lecture this semester. 	He genuinely cares for his students and their ability to succeed. on bcourses. MATH 54 Linear Algebra and (4)  NOTE: STAT 20 at Berkeley has a prerequisite of one semester of calculus. Department of Mathematics, UC Davis · One Shields Ave · Davis, CA 95616 · (530) 752-0827. CBE Thermal Comfort tool to calculate thermal comfort according to ASHRAE Standard 55-2017, ASHRAE standard 55 thermal comfort tool, thermal comfort, PMV, PPD, SET, Adaptive comfort, Center for the Built Environment, CBE, UC Berkeley, Predicted Mean Vote, Predicted Percentage of Dissatisfied, Standard Equivalent Temperature, Ole Fanger, Richard de Dear, Gail Brager, Draft, Draught, Air. Still, 200 seconds is a lot. All About Ratios Table of Contents. Chemistry majors who receive a grade of D+ or lower in a chemistry course for which a grade of C- or higher is required must repeat the course at UC Berkeley. Fun: Confess. Match made on Care. Scholze in Fall 2014 at UC Berkeley. 0 United States License. fall spring fall spring fall spring fall spring math 1a math 1b math 53 math 54 me 104 me 100 me 103** me 102b 4 4 4 4 3 4 4 4 chem 1a/l or phys 7a phys 7b me 40 me 106 me 109 me tech elec me tech elec. 23 x 10-4 = 0. Annals of Mathematics Fine Hall – Washington Road Princeton University Princeton, NJ 08544, USA Phone: 1-609-258-6468, Fax: 1-609-258-1367. Use margins for questions, comments, notes to yourself on unclear material, etc. All the GSIs know what is going on. 		A note about writing. 22 These findings also explain why studies using only high doses of. Founded in 1868 on the San Francisco Bay, UC Berkeley is the flagship campus of the University of California and one of the world's most prestigious public universities. MIT Mathematics Council, 2013-2015, 2016-17, 2018-19. I think I'll be okay with my two breadth classes (can take one of them p/np but not the other) but since I got a C- in Math 1B and a B in 61A I need to get good grades in the rest of the CS prereqs. MATHEMATICS OF DOPING PROFILES The diffusion equation with constant D : ð¶C(x,t) ð¶t = D ð¶2C(x,t) ð¶x2 has the general solution: C(x,t) =. 090909 Only fractions in lowest terms are listed. We officially assume no prerequisites other than a little calculus (at the level of Math 1A), though we will also appeal to Math 53, 54, and 55 for a few examples. We say '3 choose 2' and write 3_C_2. Supplement those with problems from the book. This is a combination of two textbooks specifically for this course. , a long-time member of the AAS, died in San Jose, California on 13 July 1996, following a long illness. Tau Beta Pi Engineering Honor Society, California Alpha Chapter. During this turbulent time, Maths 261AB were cancelled two years in a row. Math 54 does the same with Fourier transforms and PDEs. George Melvin's Math 54 webpage. Welcome to Math 54! This fantastic course is an introduction to linear algebra and its applications to differential equations. While there are a number of credit cards currently offering 100,000 point welcome bonuses, not every point is worth the same amount. because I plan on taking 1B if I end up attending Berkeley. 	You will be able to declare Computer Science as your major when you complete your remaining technical prerequisites with a Berkeley grade point average of at least 3. The guy absolutely lives math, yes lives. O'Neil—a Harvard-trained mathematician and former hedge fund data analyst—discusses how many of the decisions that affect our lives—where we go to school, whether we get a car loan, how. University of California, Berkeley. Only courses taken at UC Berkeley count toward the GPA calculation. Engineering Mathematics and Statistics Major Program, Undergraduate. MATH 54 Home Updates Contact Homeworks Welcome folks! Summer 2018 UC Berkeley. I Are the following functions are linearly independent fit 14 get Is htt 1 Solution Tocheckindependence a. Linear Algebra and Differential Equations, Second Custom Edition for UC Berkeley, by Lay, Nagle, Saff and Snider. Schedule: There will be lectures two days a week, TTh 5:00-6:30, in Moffitt Library 145. If you were admitted to UC Berkeley before Fall 2015: Complete these prerequisites: Math 1A, Math 1B, Math 54, CS 61A, CS 61B, CS 61C, CS 70. 4805 for more information. and Cathleen D. Note: Effective Fall 2019, Math 1A and Math 1B cannot be taken after completing Math 53 and/or Math 54 at UCB to increase the math prerequisite GPA. For instance, to find 2/8, first simplify it to 1/4 then search for it in the table below.


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# Find the sum of the series $S = \sum_{k=1}^{n} \frac{k}{k^{4} + k^{2} + 1}$

$$S = \sum_{k=1}^{n} \frac{k}{k^{4} + k^{2} + 1}$$

I started by factorizing the denominator as $k^2+k+1$ and $k^2-k+1$ The numerator leaves a quadratic with $k$ and $k-1$ or a constant with $k+1$ and $k-1.$ I tried writing the individual terms, ofcourse, it was useless. How do I do this?

• After you factor the denominator and use partial fractions, I believe the sum will telescope. Nov 30 '17 at 14:41
• As a rule, we don't use $\sum_{n=1}^{n}$. We use two different variables: $\sum_{k=1}^{n}\dots$. Also, you *really don't need any of those parantheses. Nov 30 '17 at 14:44
• Nov 30 '17 at 17:30

So your term is equal to $$\frac{1}{2}\left(\frac{1}{k^2-k+1}-\frac{1}{k^2+k+1}\right)$$
Now note $(k+1)^2-(k+1)+1=k^2+k+1$, so your term is: $$\frac{1}{2}\left(\frac{1}{k^2-k+1}-\frac{1}{(k+1)^2-(k+1)+1}\right)$$
and you can apply a telescoping series technique to establish the sum to $n$ is just half of $\frac{1}{1^2 -1 +1}-\frac{1}{(n+1)^2-(n+1)+1}$. And if you are also looking for the limit, half of $\frac{1}{1^2 -1 +1}$.
• Note that if you didn't recognize that $(k+1)^2-(k+1)+1=k^2+k+1$, you can discover it by noticing that the roots of $x^2-x+1=0$ - namely, $\frac12(1\pm\sqrt{-3})$ - are exactly 1 more than the roots of $x^2+x+1=0$, $\frac12(-1\pm\sqrt{-3})$. Dec 1 '17 at 17:06

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# Thread: Explain the integral of tan...

1. ## Explain the integral of tan...

Hi

my book says the integral of tan x = ln |sec x|

When i do it:

tan x = sin x/cos x

integral sinx/cos x dx

let u = cos x
du = -sin x dx
- du = sin x dx

integral: -(1/u) du

= ln u = -ln cos x

but sec x = 1/cos x

...?

Edit:

Nvm figured it out -.-

- ln cos x = ln cos x^-1
= ln sec x

so they are equivalent....duh

2. There is nothing wrong with your mathematics, so your book must be wrong: integral tanx dx - Wolfram|Alpha

Looks like you are right.

3. The book is saying the same thing he is and the same thing Wolfram is:
$-ln|cos(x)|= ln|\frac{1}{cos(x)}|= ln|sec(x)|$
(Plus a constant, of course.)


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##### Well-Known Member
Log Member
Just saw this. Will paypal you this evening.

#### Victor Bravo

##### Well-Known Member
It might be very helpful to have some idea of how many of which pieces are included.

1100 washers, 50 nuts, and 10 bolts may not be what the buyer thinks is quite so valuable. 1000 bolts and 150 nuts and 10 washers may be the best deal of the century.

As the great Alanis Morrissette has so eloquently advised the buyer... "you ought to know"

##### Well-Known Member
Log Member
It might be very helpful to have some idea of how many of which pieces are included.

1100 washers, 50 nuts, and 10 bolts may not be what the buyer thinks is quite so valuable. 1000 bolts and 150 nuts and 10 washers may be the best deal of the century.

As the great Alanis Morrissette has so eloquently advised the buyer... "you ought to know"
VB I sent the seller the exact same question earlier tonight...

#### airbike

##### Well-Known Member
Log Member
1,160 pieces of bolts from AN3 thru AN27 and stop nuts and washers for $175.00 1,160 Bolts and stop nuts and washers !!! Postage$8.00
Today it is in mail. Heavy box!


text:
# Electronic – How to Calibrate 32.768kHz crystal for PIC24 RTCC

calibrationcrystalpicrtc

I'm trying to figure out the best method for PIC24 RTCC crystal calibration.
Their application note states two methods: using a lookup table and using a reference system clock.

According to them the reference system clock method is best, but they recommend a system oscillator that is a multiple of the RTCC crystal oscillator, like 16.777MHz.

Has anyone actually tried this RTCC crystal calibraiton process for PIC24?
I would appreciate some practical guidelines.
I'm using PIC24FJ128GA006.

Calibrating against the mains frequency, as Tony suggests, is a bad idea. Long-time accuracy may be good, short-time accuracy isn't.

edit
Tony is dismissive about my reference, but that's no problem, there are other sources which confirm this. (Note that he does use my reference to show an absolute accuracy of 10 mHz/50 Hz = 0.1 ppm (sic). It looks like he is so preoccupied with his 10\$^{-10}\$ that he doesn't see a factor thousand error.) Maybe he accepts the authority of the ENTSOE, that's the "European Network of Transmission System Operators for Electricity". They should know. From this document:

Activation of PRIMARY CONTROL. PRIMARY CONTROL activation is triggered before the FREQUENCY DEVIATION towards the nominal frequency exceeds \$\pm\$20 mHz.

Maximum Permissible Quasi-Steady-State Frequency Deviation after Reference Incident. A quasi-steady-state FREQUENCY DEVIATION of \$\pm\$180 mHz away from the nominal frequency is permitted as a maximum value in the UCTE SYNCHRONOUS AREA after occurrence of a reference incident after a period of initially undisturbed operation. When assuming that the effect of self-regulation of the load is absent, the maximum permissible quasi-steady-state deviation would be \$\pm\$200 mHz.

This site gives you a real-time view of the deviation.

Even if we ignore the 200 mHz incidents there are still the 20 mHz deviations. We're talking about 400 ppm, that's more than an order of magnitude than the error of the uncalibrated crystal. 4000 ppm or two orders of magnitude taking the reference incidents into account. So the conclusion remains the same: the line frequency's short-term accuracy is by no means good enough to calibrate a crystal.
end of edit

The graph shows that a 50Hz mains frequency continuously fluctuates between 49.9Hz and 50.1Hz, that's a 0.2% error, or 2000ppm. An uncalibrated watch crystal is 20ppm accurate. (Horizontal scale is days.)

This device may be of help:

It's a Chip Scale Atomic Clock which outputs a 10MHz square wave with 1.5 \$\times\$ 10\$^{-10}\$ accuracy, several orders of magnitude more accurate than TCXO (Temperature Controlled Crystal Oscillator). Tune your oscillator so that you get 10 000 000 pulses from the CSAC over 32 768 cycles of your crystal.

Only 1500 dollar, which sounds like a bargain to me. (Your own fault, you should have mentioned a budget :-))

edit
Cheaper? OK, this OCXO (Oven Controlled Crystal Oscillator) has 5ppb (0.005ppm) frequency stability and less than 0.1ppm aging per year. About 150 dollar. Available in 16.384MHz, which is a multiple of 32.768kHz (500x). You mentioned this in your question, though there's really no reason for this.

Some GPS receivers have a 1 PPS (Pulse Per Second) output, which should have high accuracy as well. You would have to count cycles of your own 32.768 kHz clock over at least 30 seconds to get at 1 ppm accuracy. Ideally a single second will get you 32 768 counts \$\pm\$1 count, which is only a 30 ppm resolution.


text:
# A Friendship Meet Cute Cup Of Jo

If you are looking for the answer of A Friendship Meet Cute Cup Of Jo, you've got the right page. We have approximately 10 FAQ regarding A Friendship Meet Cute Cup Of Jo. Read it below.

## A recipe for tropical punch calls for 2 cups of

Ask: A recipe for tropical punch calls for 2 cups of pineapple juice and 3 cups of orange juice. Jo creates a drink by mixing 3 cups of pineapple juice with 4,cups of orange juice.
How does Jo's drink compare to the tropical punch recipe?

Jo's drink has more pineapple juice than the tropical punch recipe.

Step-by-step explanation:

$$= \frac{3}{4} - \frac{2}{3} \\ = \frac{9}{12} - \frac{8}{12} \\ = \frac{1}{12}$$

## Daisy, jo and Flor have P268 together, jo has 15

Ask: Daisy, jo and Flor have P268 together, jo has 15 less than Daisy and Flor has twice as much money as jo. How much money do Daisy and jo have together?

Step-by-step explanation:

Here's the list of the money that each of them have. Let x be the money of Daisy.

Daisy = x

Jo = x - 15

Flor = 2(x - 15)

Solution:

Getting the amount of money that Daisy (x) have.

x + x - 15 + 2(x - 15)= 268

x + x - 15 + 2x - 30 = 268

4x - 45 = 268

4x = 268 + 45

4x = 313

4x/4 = 313/4

x = 78.25

Getting the amount of money Jo (x - 15) has by substitution.

Jo = x - 15

Jo = 78.25 - 15

Jo = 63.25

78.25 + 63.25 = 141.5

Therefore, Daisy and Jo have money of P141.5 together.

#BrainlySummerChallege

## ❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤join the meeting on go ogle Meet for friendship.cgc-gnho-daw

Ask: ❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤join the meeting on go ogle Meet for friendship.
cgc-gnho-daw

❤❤❤❤❤❤❤❤Huh?

## 8. Complete this saying, "Art is where work meetsA. HopeB.

Ask: 8. Complete this saying, "Art is where work meets
A. Hope
B. Peace
C. Love
D. Friendship

C. Love

Explanation:

Hope it helpssss

8. C. LOVE

IT helpsssssss

## Do you agree with Aristotle's point of view that friendship

Ask: Do you agree with Aristotle's point of view that friendship of excellence is the least changeable and most lasting form of
friendship compared to the friendship of pleasure and friendship of utility? Why or Why not?

Friendship, as understood here, is a distinctively personal relationship that is grounded in a concern on the part of each friend for the welfare of the other, for the other’s sake, and that involves some degree of intimacy. As such, friendship is undoubtedly central to our lives, in part because the special concern we have for our friends must have a place within a broader set of concerns, including moral concerns, and in part because our friends can help shape who we are as persons. Given this centrality, important questions arise concerning the justification of friendship and, in this context, whether it is permissible to “trade up” when someone new comes along, as well as concerning the possibility of reconciling the demands of friendship with the demands of morality in cases in which the two seem to conflict.

Explanation:

## if PJ=2x,JO=x+10, and PO=40, find JO

Ask: if PJ=2x,JO=x+10, and PO=40, find JO

To get JO, subtract the distance of PJ to the PO.

40-25=15

JO=15

Step-by-step explanation:

A recipe for tropical punch calls for 2 cups of pineapple juice and 3 cups of orange juice. Jo creates a drink by mixing 3 cups of pineapple juice with 4 cups of orange juice.
How does Jo's drink compare to the tropical punch recipe?

I think it's 2 cups

Because i added the 2 and 3 and the 3 and 4 and subtract them hopefully it was right and im sorry if im wrong

## Do you agree with Aristotle's point of view that friendship

Ask: Do you agree with Aristotle's point of view that friendship of excellence is the least changeable and most lasting form of
friendship compared to the friendship of pleasure and friendship of utility? Why or Why not?

Rather than utility or pleasure, this kind of relationship is based on a mutual appreciation of the virtues that the other party holds dear. ... They're pleasurable and beneficial. When you respect a person and care for them, you gain joy from being with them.

Explanation:

## sangkap ng pakikipagkaibigana.fabric of friendshipb.heart of friendshipc.empathyd.katapatane.condidentialityf.preperensiyapagbibigay ng panahon upang

a.fabric of friendship
b.heart of friendship
c.empathy
d.katapatan
e.condidentiality
f.preperensiya

pagbibigay ng panahon upang pisikal na magkasama

a.fabric of friendship
b.heart of friendship
c.empathy
d.katapatan
e.condidentiality
f.preperensiya

paglalagay ng iyong sarili sa kanyang katayuan

a.fabric of friendship
b.heart of friendship
c.empathy
d.katapatan
e.condidentiality
f.preperensiya

pagtitimpi na ibahagi ang mga lihim na bagay

a.fabric of friendship
b.heart of friendship
c.empathy
d.katapatan
e.condidentiality
f.preperensiya

ganap na pagbabahagi sa isat isa sa tunay na niloloob

a.fabric of friendship
b.heart of friendship
c.empathy
d.katapatan
e.condidentiality
f.preperensiya

b

d

a

d

d

Sana makatulong po ito sa inyo

## Online friendshipSimilaritiesOffline friendship

Similarities
Offline friendship


text:
co-log-polysemy-0.0.0.0: Composable Contravariant Comonadic Logging Library

Colog.Polysemy.Effect

Description

This module contains logging effect which can be interpreted in terms of LogAction from the co-log-core package.

Synopsis

Effect

data Log (msg :: Type) (m :: Type -> Type) (a :: Type) where Source #

Effect responsible for logging messages of type msg. Has similar structure to LogAction.

You can think of this effect in the following way in terms of the existing effects in polysemy:

1. Like Output but specialised for logging.
2. Like Trace but polymorphic over logged message.

Constructors

 Log :: msg -> Log msg m ()

Actions

Arguments

 :: Member (Log msg) r => msg Message to log -> Sem r () Effectful computation with no result

Log a message. If you semantic monad Sem has effect Log then you can send messages of type msg to that effect. This function can be used like this:

application :: Member (Log String) r => Sem r ()
application = do
log "Application started..."
log "Application finished..."

Interpretations

runLogAction :: forall m msg r a. Member (Lift m) r => LogAction m msg -> Sem (Log msg ': r) a -> Sem r a Source #

Run a Log effect in terms of the given LogAction. The idea behind this function is the following: if you have LogAction m msg then you can use this action to tell how to io interpret effect Log. However, this is only possible if you also have Lift m effect because running log action requires access to monad m.

This function allows to use extensible effects provided by the polysemy library with logging provided by co-log. You can construct LogAction independently and then just pass to this function to tell how to log messages.

Several examples:

1. runLogAction mempty: interprets the Log effect by ignoring all messages.
2. runLogAction logStringStdout: interprets Log effect by allowing to log String to stdout.

runLogAsTrace :: forall r a. Member Trace r => Sem (Log String ': r) a -> Sem r a Source #

Run Log as the Trace effect. This function can be useful if you have an interpreter for the Trace effect and you want to log strings using that interpreter.

runLogAsOutput :: forall msg r a. Member (Output msg) r => Sem (Log msg ': r) a -> Sem r a Source #

Run Log as the Output effect. This function can be useful if you have an interpreter for the Output effect and you want to log messages using that interpreter.

Interpretations for Other Effects

runTraceAsLog :: forall r a. Member (Log String) r => Sem (Trace ': r) a -> Sem r a Source #

Run Trace as the Log effect. This function can be useful if you have an interpreter for the Log effect and you want to log strings using that interpreter.

runOutputAsLog :: forall msg r a. Member (Log msg) r => Sem (Output msg ': r) a -> Sem r a Source #

Run Output as the Log effect. This function can be useful if you have an interpreter for the Log effect and you want to log messages using that interpreter.


text:
Search: All articles in the CJM digital archive with keyword moduli space of flat $G$ connections
 On the Connectedness of Moduli Spaces of Flat Connections over Compact Surfaces We study the connectedness of the moduli space of gauge equivalence classes of flat $G$-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the compact, connected, simply connected Lie groups, and some non-semisimple classical groups. Keywords:moduli space of flat $G$ connectionsCategory:53


text:
# Ideal Gas Law

Written by Jerry Ratzlaff on . Posted in Thermodynamics

The ideal gas law can be used to predict pressure, temperature & volume changes in ideal gasses.  An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces.  In the real world, the ideal gas law must be corrected but it can serve as a good approximation for initial calculations.

## Ideal Gas Law formula

 $$\large{ p \; V = n \; R \; T }$$

### Where:

 Units English Metric $$\large{ p }$$ = pressure of gas $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$ $$\large{ \rho }$$ (Greek symbol rho) = density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$ $$\large{ n }$$ = number of moles of gas $$\large{dimensionless}$$ $$\large{ R }$$ = specific gas constant (gas constant) $$\large{\frac{ft-lbf}{lbm-R}}$$ $$\large{\frac{J}{kg-K}}$$ $$\large{ T }$$ = temperature of gas $$\large{ R }$$ $$\large{ K }$$ $$\large{ V }$$ = volume of gas $$\large{ in^3 }$$ $$\large{ mm^3 }$$

### Solve For:

 $$\large{ \rho = \frac{ p }{R \; T} }$$ $$\large{ p = \frac{n \; R \; T}{V} }$$ $$\large{ p = \rho \; R \; T }$$ $$\large{ n = \frac{ p \; V}{R \; T} }$$ $$\large{ R = \frac{ p }{ \rho \; T } }$$ $$\large{ T = \frac{ p \; V}{n \; R} }$$ $$\large{ T = \frac{ p }{ \rho \; R } }$$ $$\large{ V = \frac{ n \; R \; T}{p} }$$

## notes

• Temperature is always the absolute temperature which will be either Rankine or Kelvin. For values that are in Fahrenheit, the conversion is °F - 459.67 = R. For values that are in Celsius the conversion is °C - 273 = K.
• Pressure is absolute pressure, not gauge pressure.
• Make sure units match on the universal gas constant.


text:
Release Notes
Algorithm Development
How to Contribute
References

# Creating a New (Complex) Algorithm

In this section, we will explain the steps for creating a more complicated algorithm (for vertically partitioned data) in Python.

In the previous section, we saw how to create a simple algorithm in the Vantage. However,it only explains the essence. Algorithms trend to be more complex. In this section, we will explain the steps to create a more complicated algorithm, which includes an iterative process (e.g., for loop) between the central server and the nodes, in Python.

# Scenario

For this example, we will consider the scenario in which we wish to analyse vertically-partitioned data from two different parties (Fig. 1). Namely, we want to obtain a regression model's $\beta$ coefficients. However, adapting the steps presented here for the horizontally-partitioned case is straightforward.

Fig. 1. Vertically-partitioned data. In this case, parties have different features from the same instances (i.e., patients).

# Assumptions

We will assume the following:

1. It is possible to mathematically decompose the algorithm in a distributed fashion.

2. Data across parties is aligned (i.e., patient 1 is in row 1 of all data partitions, patient 2 is in row 2 of all data partitions, and so on). This assumption is crucial for vertically-partitioned data.

3. Data have been pre-processed appropriately (i.e., data are clean and column names match).

# Standardizing IO

The algorithm will receive input parameters in a txt file. Furthermore, it will write the output to a txt file too. Both of these files will be located in the /app/ directory (i.e., /app/input.txt and app/output.txt. In order to keep maximum flexibility, JSON format must also be used as input/output format for all functions.

When passing strings in a JSON, use double quotes ("string" ) and not single quotes ('string') since the latter are not JSON compliant.

You cannot send numpy arrays in JSON. Thus, when you need to send one, be sure to:

1. Convert it to a list (e.g., numpy_array.tolist())

2. Pack it into the JSON

3. Send it to a function

4. Receive it in the function

5. Convert it back to a numpy array (e.g., np.array(a_list))

Take algorithm_nodes as an example.

The txt-files are likely to be replaced by a more robust system in the future.

## Environment variables

The following environment variables need to be available to the algorithm:

 Variable name Description DATABASE_URI Path to the data file (e.g., csv file). Of course, this path will change for each party (i.e., node). HOST Host name and protocol (http/https) of the central server API_PATH Api path of the central server PORT Port to which the central server listens

From version 0.3.0 the same environment variables will be used, however the host, api_pathand port point towards a local proxy server as the algorithm container no longer has internet access.

# The algorithm

We will need to create at least four different files (of course, in your case you could have more [supporting] files):

1. main.py

2. master.py

3. algorithm_central.py

4. algorithm_nodes.py

5. Dockerfile

6. requirements.txt

Let's go in detail through each of these: what they are supposed to do and how are they supposed to be structured.

## main.py

This file is the main entry-point for the Docker container. Furthermore, it will also trigger the execution of the algorithm in the Docker container. Let's look at it in detail.

You can think of a Docker image as a template/blueprint. You can think of a Docker container as an instance of such template.

First, some standard imports

import sysimport json

Then, we need to import the functions that will be triggered in the master container and in the nodes.

# Central serverfrom master import master# Nodesfrom algorithm_nodes import(    count_patients,    compute_conjugate_matrix,    update_beta )

Notice that although there are more functions that are called in the master container, these are all called by the master function, which is the one that is triggered. A master container is an instance of a docker image which triggers the master function.

For convenience, we will also quickly define a couple of functions to display information to the console and to store in the log-file. These functions are particularly useful when debugging your code:

info = lambda msg: sys.stdout.write("info > " + msg + "\n")warn = lambda msg: sys.stdout.write("warn > " + msg + "\n")

Afterwards, we will read the input to the algorithm from the file input.txt (as defined previously):

info("Reading input...")with open("app/input.txt") as fp:    input_ = json.loads(fp.read())

In the next step, we need to define which function will be triggered. When the user makes a request to run the algorithm, it will trigger the master function. When the algorithm is running, it will trigger the corresponding node functions. This looks as follows:

method_name = input_.get("method", "master")method = {    "master": master,    "count_patients": count_patients,    "compute_gram_matrix": compute_conjugate_matrix,    "update_beta": update_beta}.get(method_name, None)# if no method was found, end executionif not method:    warn(f"Method '{method_name}' not found!\n")    exit()# read method's argumentsargs = input_.get("args", [])kwargs = input_.get("kwargs", {})

The convention for defining the keys in the method dictionary is using snake case (i.e.,  lowercase_separated_by_underscores). Please avoid any other casing!

Then, we will actually call the function. Notice how the prototype for all functions is the same (method(*args, **kwargs)), except for the master function, which requires a token as an input too.

if method_name == "master":    info("Reading token...")    with open("app/token.txt") as fp:        token = fp.read().strip()        info(token)        output = method(token, *args, **kwargs)    else:     output = method(*args, **kwargs)

Finally, we will write the output as a txt-file:

info("Writing output...")with open("app/output.txt", 'w') as fp:    fp.write(json.dumps(output))

## master.py

This file will do the heavy lifting. It will coordinate the flow of the algorithm between the central server and the nodes as a researcher would do. Let's look at it a little bit closer.

First, the imports:

import sysimport osimport jsonimport timeimport algorithm_centralfrom pytaskmanager.node.FlaskIO import ClientContainerProtocol

For now don't worry about pytaskmanager.node.FlaskIO. It will be installed in the Docker container later on. The import pytaskmanager will change in version 0.3.0.

Then, we will define the parameters of the algorithm execution:

ITERATIONS = 10 # Max number of iterations waiting for convergence. TOLERANCE = 1e-8 # Tolerance limit for convergence.

Just like in main.py, we will define a couple of functions for printing in the console.

info = lambda msg: sys.stdout.write("info > " + msg + "\n")warn = lambda msg: sys.stdout.write("warn > " + msg + "\n")

Afterwards, we will define a master function, which will contain the workflow of the algorithm. Its prototype will be master(token, organization1_id, organization2_id) , which can be extended to as many organizations (i.e., parties, nodes) as necessary. In this case, for the sake of simplicity we will only consider two.

Inside master, the first thing is to set up the connection client. We can do so like this:

client = ClientContainerProtocol(    token = token,     host = os.environ["HOST"],    port = os.environ["PORT"],     path = os.environ["API_PATH"])

For convenience, we will define the names of the columns of interest of each party (node).

columns1 = ['feat1', 'feat2', 'feat3']columns2 = ['featA', 'featB', 'featC']n_features = len(columns1 + columns2)

In the code-block above the column-names are hard coded. This is not ideal, as now you have to rebuild the entire image if different column-names are used. A better solution would be to supply these as input to the master method.

Suppose that our algorithm requires counting the number of patients at each node. After that, we need to compute the conjugate of the feature matrix at each node, too. Every time that we want to execute a function in a node, we need to create a task and wait for its results. This would result in the following code:

info("Computing number of patients...")patients_tasks = []for [columns, organization_id] in zip([columns1, columns2], [organization1_id, organization2_id]):    new_task = client.create_new_task(            input_ = {                    "method": "count_patients",                    "args": [columns],                    "kwargs": {}            },            organization_ids = [organization_id]            )    patients_tasks.append(new_task)info("Waiting for number of patients count...")patients1 = wait_for_results(client, patients_tasks[0])patients2 = wait_for_results(client, patients_tasks[1])info("Computing conjugate matrices...")conjugate_tasks = []for [columns, organization_id] in zip([columns1, columns2], [organization1_id, organization2_id]):    new_task = client.create_new_task(            input_ = {                    "method": "compute_conjugate_matrix",                    "args": [columns],                    "kwargs": {}            },            organization_ids = [organization_id]            )    conjugate_tasks.append(new_task)info("Waiting for local gram matrices computation...")conjugate1= wait_for_results(client, conjugate_tasks[0])conjugate2 = wait_for_results(client, conjugate_tasks[1])

The function wait_for_results is defined outside master and looks like this:

def wait_for_results(client, task):    task_id = task.get("id")    task = client.request(f"task/{task_id}")    while not task.get("complete"):        task = client.request(f"task/{task_id}")        info("Waiting for results...")        time.sleep(1)    info("Obtaining results...")    results = client.get_results(task_id = task.get("id"))    results = [json.loads(result.get("result")) for result in results]    if len(results) == 1:        results = results.pop()    return results

It is worth mentioning something important here. The way the code is now, we would first ask for the number of patients, wait for the results, ask for the conjugate matrices, and wait for the results. However, these two processes are independent of each other. In other words, we don't need the number of patients to compute the conjugate matrices. Therefore, we can improve the performance of our code by doing a little bit of reshuffling:

info("Computing number of patients...")patients_tasks = []for [columns, organization_id] in zip([columns1, columns2], [organization1_id, organization2_id]):    new_task = client.create_new_task(            input_ = {                    "method": "count_patients",                    "args": [columns],                    "kwargs": {}                    },            organization_ids = [organization_id]            )    patients_tasks.append(new_task)   info("Computing conjugate matrices...")conjugate_tasks = []for [columns, organization_id] in zip([columns1, columns2], [organization1_id, organization2_id]):    new_task = client.create_new_task(            input_ = {                    "method": "compute_conjugate_matrix",                    "args": [columns],                    "kwargs": {}                    },            organization_ids = [organization_id]            )    conjugate_tasks.append(new_task)info("Waiting for number of patients count...")patients1 = wait_for_results(client, patients_tasks[0])patients2 = wait_for_results(client, patients_tasks[1])info("Waiting for local gram matrices computation...")conjugate1= wait_for_results(client, conjugate_tasks[0])conjugate2 = wait_for_results(client, conjugate_tasks[1])

When implementing your algorithm, keep in mind which steps need to be done sequentially and which steps can be done in parallel and order your code accordingly.

Now, let's suppose that our algorithm needs to obtain the sum of the conjugate matrices. This operation is done in the master container as follows:

info("Computing global conjugate matrix...")K = algorithm_central.compute_global_conjugate_matrix([    conjugate1,    conjugate2 ])['K']

Finally, let's suppose that the algorithm will make an initial guess of the $\beta$ coefficients and will update this value iteratively depending on the global conjugate matrix and the data of at each node. It will stop updating after a certain number of iterations has been reached (defined earlier as ITERATIONS) or when the change between the coefficients is less than TOLERANCE (i.e., when $\beta$ coefficients have converged). We can do this using the following code:

info(f"Preparing {ITERATIONS} iterations...")coefficients = {} # Initialize variables.coefficients['beta_init'] = 0.5 * np.ones((n_features , 1)) # Initial guess.info(f"Computing betas...")   for s in range(0, ITERATIONS):    info(f"Iteration {s}")    if s == 0:        beta_old = coefficients['beta_init']     else:        beta_old = beta    info("Computing local beta...")    beta_tasks = []    for [columns, organization_id] in zip([columns1, columns2], [organization1_id, organization2_id]):        new_task = client.create_new_task(                input_ = {                        "method": "update_beta",                        "args": [                                columns,                                K,                                beta_old.tolist()                                ],                        "kwargs": {}                        },                organization_ids = [organization_id]                )        beta_tasks.append(new_task)        info("Waiting for local E matrices computation...")    beta1 = wait_for_results(client, beta_tasks[0])    beta2 = wait_for_results(client, beta_tasks[1])    beta = beta1 + beta2        # Check for convergence    if max(abs(beta - beta_old)) < TOLERANCE:        info(f"Convergence reached at iteration {s}")        break# Final alpha value.coefficients['beta_final'] = beta

## algorithm_central.py

In this file, we will define the (mathematical) functions that will be executed by the master container. For our example, this file would look something like this.

We will start with the same basics as before: imports and a couple of functions for printing to the console.

import sysimport numpy as npinfo = lambda msg: sys.stdout.write("info > " + msg + "\n")warn = lambda msg: sys.stdout.write("warn > " + msg + "\n")

Afterwards, we will define all the actual functions. In our example, this was the function compute_global_conjugate_matrix

def compute_global_conjugate_matrix(nodes_conjugate_matrix):    # Initialize global conjugate matrix.    K = np.zeros(np.array(nodes_conjugate_matrix[0]['K']).shape)        # Add nodes' gram matrices.    for node_conjugate_matrix in nodes_conjugate_matrix:        K += node_conjugate_matrix ['K']        return {'K': K.tolist()}

## algorithm_nodes.py

In this file, we will define the (mathematical) functions that will be executed by the nodes. For our example, this file would look something like this.

We will start with the same basics as before: imports and a couple of functions for printing to the console.

import sysimport osimport pandas as pdimport numpy as npinfo = lambda msg: sys.stdout.write("info > " + msg + "\n")warn = lambda msg: sys.stdout.write("warn > " + msg + "\n")

Afterwards, we will define all the actual functions. In our example, these were the functions count_patients, compute_conjugate_matrix, and update_beta

def count_patients(column_names):    # Read data.    path = os.environ["DATABASE_URI"]    X = pd.read_csv(path)[column_names].to_numpy()        # Compute number of patients.    M = len(X)        return {'M': M}
def compute_conjugate_matrix(column_names):       # Read data.    path = os.environ["DATABASE_URI"]    X = pd.read_csv(path)[column_names].to_numpy()        # Compute conjugate matrix    K = np.conjugate(X).tolist()        return {'K': K}
def update_beta(columns, K, beta_old):    # Read data.    path = os.environ["DATABASE_URI"]    data = pd.read_csv(path)[columns].to_numpy()        # Convert from list to     beta_old = np.asarray(beta_old)        # Compute new value of beta as a function of data, K, and old beta.        beta_new = ...    return beta_new.tolist()

# Dockerizing the algorithm

Finally, just like in the previous example, we will dockerize the algorithm and push it to a registry from which the nodes can retrieve the algorithms. To do so, we need to generate a requirements.txt where we specify which packages are needed:

requirements.txtpandasnumpyppdli

Then, we will generate a Dockerfile, which dictates the how the Docker image is build.

Dockerfile# Choose Python 3 image as base.FROM python:3# Copy the requirements file to the image.COPY requirements.txt /app/requirements.txt# Install algorithm dependencies.RUN pip install --no-cache-dir -r /app/requirements.txt# Copy all local files to the image.COPY . /# Execute the algorithm in the container.CMD ["python", "./main.py"]

Note that we first copy requirements.txt and install the dependencies and then copy all other project files. This way if we make an update to the code, not the entire docker image is rebuild, which safes us a lot of time when developing.

Now a docker-image can be created from our project using this docker-recipe, and we can push it to the registry:

docker build -t docker-registry.distributedlearnin.ai/d_algorithm_name .docker push docker-registry.distributedlearnin.ai/d_algorithm_name

# Final remarks

You can see the final versions of each file below:

main.py
master.py
algorithm_central.py
algorithm_nodes.py
requirements.txt
Dockerfile
main.py
# -*- coding: utf-8 -*-"""master.py"""#%% Preliminaries.import sysimport json# Central serverfrom master import master# Nodesfrom algorithm_nodes import(    count_patients,    compute_conjugate_matrix,    update_beta )info = lambda msg: sys.stdout.write("info > " + msg + "\n")warn = lambda msg: sys.stdout.write("warn > " + msg + "\n")#%%info("Reading input...")with open("app/input.txt") as fp:    input_ = json.loads(fp.read())    #%% Determine function and its corresponding args and kwargs from input.method_name = input_.get("method", "master")method = {    "master": master,    "count_patients": count_patients,    "compute_gram_matrix": compute_conjugate_matrix,    "update_beta": update_beta}.get(method_name, None)# If no method was found, end execution.if not method:    warn(f"Method '{method_name}' not found!\n")    exit()# Define method's parameters.args = input_.get("args", [])kwargs = input_.get("kwargs", {})#%% Actually call the function.if method_name == "master":    info("Reading token...")    with open("app/token.txt") as fp:        token = fp.read().strip()        info(token)        output = method(token, *args, **kwargs)    else:     output = method(*args, **kwargs)#%%info("Writing output...")with open("app/output.txt", 'w') as fp:    fp.write(json.dumps(output))
master.py
# -*- coding: utf-8 -*-"""master.py"""#%% Preliminaries.import sysimport osimport jsonimport timeimport numpy as npimport algorithm_centralfrom pytaskmanager.node.FlaskIO import ClientContainerProtocolITERATIONS = 10 # Max number of iterations waiting for convergence.TOLERANCE = 1e-8 # Tolerance limit for convergence.info = lambda msg: sys.stdout.write("info > " + msg + "\n")warn = lambda msg: sys.stdout.write("warn > " + msg + "\n")#%%def master(token, organization1_id, organization2_id):    client = ClientContainerProtocol(        token = token,         host = os.environ["HOST"],        port = os.environ["PORT"],         path = os.environ["API_PATH"]    )        columns1 = ['feat1', 'feat2', 'feat3']    columns2 = ['featA', 'featB', 'featC']    n_features = len(columns1 + columns2)    info("Computing number of patients...")    patients_tasks = []    for [columns, organization_id] in zip([columns1, columns2], [organization1_id, organization2_id]):        new_task = client.create_new_task(                input_ = {                        "method": "count_patients",                        "args": [columns],                        "kwargs": {}                        },                organization_ids = [organization_id]                )        patients_tasks.append(new_task)       info("Computing conjugate matrices...")    conjugate_tasks = []    for [columns, organization_id] in zip([columns1, columns2], [organization1_id, organization2_id]):        new_task = client.create_new_task(                input_ = {                        "method": "compute_conjugate_matrix",                        "args": [columns],                        "kwargs": {}                        },                organization_ids = [organization_id]                )        conjugate_tasks.append(new_task)            info("Waiting for number of patients count...")    patients1 = wait_for_results(client, patients_tasks[0])    patients2 = wait_for_results(client, patients_tasks[1])        info("Waiting for local gram matrices computation...")    conjugate1= wait_for_results(client, conjugate_tasks[0])    conjugate2 = wait_for_results(client, conjugate_tasks[1])    info("Computing global conjugate matrix...")    K = algorithm_central.compute_global_conjugate_matrix([        conjugate1,        conjugate2     ])['K']            info(f"Preparing {ITERATIONS} iterations...")    coefficients = {} # Initialize variables.    coefficients['beta_init'] = 0.5 * np.ones((n_features , 1)) # Initial guess.    info(f"Computing betas...")       for s in range(0, ITERATIONS):        info(f"Iteration {s}")        if s == 0:            beta_old = coefficients['beta_init']         else:            beta_old = beta        info("Computing local beta...")        beta_tasks = []        for [columns, organization_id] in zip([columns1, columns2], [organization1_id, organization2_id]):            new_task = client.create_new_task(                    input_ = {                            "method": "update_beta",                            "args": [                                    columns,                                    K,                                    beta_old.tolist()                                    ],                            "kwargs": {}                            },                    organization_ids = [organization_id]                    )            beta_tasks.append(new_task)                info("Waiting for local E matrices computation...")        beta1 = wait_for_results(client, beta_tasks[0])        beta2 = wait_for_results(client, beta_tasks[1])        beta = beta1 + beta2                # Check for convergence        if max(abs(beta - beta_old)) < TOLERANCE:            info(f"Convergence reached at iteration {s}")            break    # Final alpha value.    coefficients['beta_final'] = beta#%%def wait_for_results(client, task):    task_id = task.get("id")    task = client.request(f"task/{task_id}")    while not task.get("complete"):        task = client.request(f"task/{task_id}")        info("Waiting for results...")        time.sleep(1)    info("Obtaining results...")    results = client.get_results(task_id = task.get("id"))    results = [json.loads(result.get("result")) for result in results]    if len(results) == 1:        results = results.pop()    return results
algorithm_central.py
# -*- coding: utf-8 -*-"""algorithm_central.py"""#%% Preliminariesimport sysimport numpy as npinfo = lambda msg: sys.stdout.write("info > " + msg + "\n")warn = lambda msg: sys.stdout.write("warn > " + msg + "\n")#%%def compute_global_conjugate_matrix(nodes_conjugate_matrix):    # Initialize global conjugate matrix.    K = np.zeros(np.array(nodes_conjugate_matrix[0]['K']).shape)        # Add nodes' gram matrices.    for node_conjugate_matrix in nodes_conjugate_matrix:        K += node_conjugate_matrix ['K']        return {'K': K.tolist()}
algorithm_nodes.py
# -*- coding: utf-8 -*-"""algorithm_nodes.py"""#%% Preliminariesimport sysimport osimport pandas as pdimport numpy as npinfo = lambda msg: sys.stdout.write("info > " + msg + "\n")warn = lambda msg: sys.stdout.write("warn > " + msg + "\n")#%%def count_patients(column_names):    # Read data.    path = os.environ["DATABASE_URI"]    X = pd.read_csv(path)[column_names].to_numpy()        # Compute number of patients.    M = len(X)        return {'M': M}        #%%def compute_conjugate_matrix(column_names):       # Read data.    path = os.environ["DATABASE_URI"]    X = pd.read_csv(path)[column_names].to_numpy()        # Compute conjugate matrix    K = np.conjugate(X).tolist()        return {'K': K}        #%%def update_beta(columns, K, beta_old):    # Read data.    path = os.environ["DATABASE_URI"]    data = pd.read_csv(path)[columns].to_numpy()        # Convert from list to     beta_old = np.asarray(beta_old)        # Compute new value of beta as a function of data, K, and old beta.        beta_new = ...    return beta_new.tolist()
requirements.txt
pandasnumpyppdli
Dockerfile
# Choose Python 3 image as base.FROM python:3# Copy the requirements file to the image.COPY requirements.txt /app/requirements.txt# Install algorithm dependencies.RUN pip install --no-cache-dir -r /app/requirements.txt# Copy all local files to the image.COPY . /# Execute the algorithm in the container.CMD ["python", "./main.py"]

Some important considerations:

You will probably be making lots of matrix operations. Watch out for your matrices' dimensionality!

If this is your first time implementing your algorithm, make sure to have validated it previously outside of the infrastructure (ideally comparing its performance against its centralized counterpart)

When communicating between the central server and the nodes, make sure you don't send raw data!

In this section, we showed how to create an iterative distributed learning algorithm (for vertically-partitioned data). We showed the required files (and their structure), workflow, and considerations in a hypothetical case. If you want to see a real-life example, take a look at our Github repository for the VERTIGO algorithm.


text:
# Create cutout of rectangle, where cutout is also node

I'm trying to overlay a picture with a semiopaque rectangle, then cut out some shapes (rectangles and circles) so the image is clear in those, then point to the cutouts with something like tikz \pin command. My problem is that the only examples i could find for cutouts use \fill and then simply pile on the cutout shapes. Is there a way to create those cutouts directly from nodes so i can later reference those nodes? Currently i am simply defining another node with the same coordinates later, to refer to that, but it would be a lot cleaner if it was possible to use the nodes for cutting directly. MWE (without nodes, from an example in the answer by Alex Recuenco in this Q: How to create a rectangle with a transparent hole):

\documentclass{article}
\usepackage{tikz}
\begin{document}

\section{Non Zero Rule}

\begin{tikzpicture}
\draw[black, fill = black, fill opacity = 0.5, semithick]
(0,0) rectangle (5,5) (2.5,2.5) circle (0.5);
\end{tikzpicture}

\section{Even Odd Rule}

\begin{tikzpicture}
% \node (image) {\includegraphics{somepic_with_cool_features}}
\draw[black, fill = black, fill opacity = 0.5, semithick, even odd rule]
(0,0) rectangle (5,5) (2.5,2.5) circle (0.5);
\end{tikzpicture}
\end{document}

To clarify: My dream would be to have something like

   % \node (image) {\includegraphics{somepic_with_cool_features}}
\draw[black, fill = black, fill opacity = 0.5, semithick, even odd rule]
(0,0) rectangle (5,5) {%
\node[pin={[red]60:Cool feature one!}] (circ1) (2.5,2.5) circle (0.5);
\node[pin={[red]60:Wow another one!}] (circ2) (4,4) circle (0.5);
\node[pin={[red]60:A whole bunch!}] (rect1) (5,6) rectangle (7,9);%
}

You can use the node boundary path for a reverse clip to protect it from being overpainted. This is very much like the eraser tool.

\documentclass{article}
\usepackage{tikz}
% based on
% https://tex.stackexchange.com/a/38995/121799
% https://tex.stackexchange.com/a/76216
% https://tex.stackexchange.com/a/59168/194703
% https://tex.stackexchange.com/q/448920/194703
\makeatletter
\tikzset{
reuse path/.code={\pgfsyssoftpath@setcurrentpath{#1}}
}
\makeatother
\tikzset{even odd clip/.code={\pgfseteorule},
protect/.code={
\clip[overlay,even odd clip,reuse path=#1]
(-5383.99999pt,-5383.99999pt) rectangle (5383.99999pt,5383.99999pt);
}}
\begin{document}

\section{Protect}

\begin{tikzpicture}
\path (2.5,2.5) node[draw,circle,save path=\pathA,minimum size=1cm](c){};
\tikzset{protect=\pathA}
\draw[overlay=false,black, fill = black, fill opacity = 0.5, semithick]
(0,0) rectangle (5,5);
\draw[stealth-] (c) -- ++ (60:1) node[above]{here};
\end{tikzpicture}
\end{document}

• can you elucidate some of what you are doing? * what's with the ultra-precision coordinates? (in an answer by Symbol 1 to the eraser-related Q tex.stackexchange.com/questions/12010/…, something like [reset cm](-\maxdimen,-\maxdimen)rectangle(\maxdimen,\maxdimen) is used - is that related? * You seem to be doing "draw node, then draw eraser-node at same coords" - that is not much less complicated than my " draw eo-cutout, then draw fakenode at same coords" - i was looking for a way to do "draw rect, now cutout node" Apr 22, 2020 at 6:36
• @bukwyrm The point of this is that you can place many of these protected nodes and add many fills and they will still not be overwritten, and have the usual anchors. Of course, if you only have a single shape and a single fill, your method is shorter. This was under the assumption that "then cut out some shapes (rectangles and circles) so the image is clear in those," means several nodes. And yes, that answer is based on many other posts which I tried to collect in the links. Basically one does an even odd clip with the path of the node and an insanely large rectangle.
– user194703
Apr 22, 2020 at 6:44
• ah! it is not about the precision (.999999) but about the size of the value? You are absolutely correct about the scalability of your method vs mine, i just wanted to point out that my dream-answer would be more succinct (in my heart of hearts i had been hoping that i had simply misread the tikz manual and was missing some parantheses or something)... Apr 22, 2020 at 6:49
• @bukwyrm The whole thing is only useful if you have a nontrivial background as in this answer. If you just want to have a filled node, you can add fill=white, say, and do not need any of this. However, when you have a nontrivial background of which you wish to "protect" some regions, and if these regions should have node anchors and a node boundary, these tools may be worthwhile.
– user194703
Apr 22, 2020 at 6:52


text:
Description

 arphilosophy.miraheze.org

I want to add this extension to my wiki, and please git clone it recursively. If adding it possible, I want also download this script to the next directory in the extension folder: MathRenderer/modules/MathJax/extensions/arabic.js . Is Adding a new font possible? if yes, may I have this font please?
I hope also that you can config the extension for me as follow (in the LocalSettings.php file):

wfLoadExtension( 'MathRenderer' ); // just a remainder to load the extension :)
$wgMRExtensions = ["arabic.js"];$wgMRUseCDN = false;
$wgMRUseChem = true;$wgMRFont = "Amiri";

Thanks a lot.

Event Timeline

Hi, we use mathoid which looks like it's incompatible with that repo.

Corey added a subscriber: Corey.Jan 9 2019, 23:12

@import url('https://fonts.googleapis.com/css?family=Amiri');

I didn't really get what you mean by "incompatible", so I'll try to hit all possibilities:

1. The extension will cause internally conflicts: I don't think it will. It just loads a MathJax script from local or remote folder (with some configurations) and sets up two hooks.
1. The extension will cause conflicts on my wiki level: I'm not totally aware of how your system works, but from what I see (on github), extensions get loaded only for specific users, so It will only conflict with Math extension on the wiki of the user that enabled both extensions. The only conflict will happen that Math extension will take over the hook of the second extension (or vice versa). It's not even a conflict.

@Corey
Hmmm, I totally forgot that I can use CSS. Thanks a lot.

I think it's somehow a hard task to accomplish on your system. What about just allow me to load scripts from this and this location? I can do the rest of magic on my Common.js page.
I repeat my thanks.

Void added a comment.Jan 17 2019, 22:15

If need be, I don't think there would be any legal reason you couldn't provide a copy of the scripts on your wiki, provided that the licensing information (which is in a comment at the top of the script) is kept intact, and that you supply the URL of the original copy.

@Void
I didn't mean in that comment asking for legal permission, but technical. I want to load them externally, using mw.loader or something similar, on my Common.js page. Doing that now gives me an error related with the CSP (Content Security Policy) in my browser console, says that the page settings blocked the loading of the resource. I just want to be able to load them.
Sorry for misunderstanding.


text:
# Jetty startup delay due to scanning

Context and setup information:

• Jetty 9 with the eclipse jetty plugin
• Spring 4.1.1.RELEASE with Spring Security 3.2.3
• Spring Java Configuration (no web.xml)

Problem description Starting jetty 9 is very slow in a project where Spring's JavaConfig is used to boot the Spring context instead of using a web.xml. Jetty seems to be doing nothing during a considerate amount of time. This occurs after the line:

INFO:oejs.Server:main: jetty-9.2.3.v20140905

Jetty does start eventually, but takes very long to start up compared to a regular tomcat 7 distribution.

    public class DispatcherServletInitializer extends AbstractAnnotationConfigDispatcherServletInitializer {
//implementation
}

This is due to the fact that Jetty 9 scans all Jars in the WEB-INF folder for annotations in order to start the web context. If you've attempted to find a solution to this problem, you probably already discovered that fact. I tried several such answers, but never found the correct solution among them.

In order to eliminate such scanning as much as possible, we can define a pattern that tells Jetty which sources to scan and which not to scan. This is done by either setting some configuration in maven, or by setting an attribute in the jetty-context.xml. (If you are using the maven plugin, you need to set Jetty's jetty-context.xml also in your pom.xml)

Some other solutions that have not worked for me (either no increase in startup time or no correct startup at all)

etc.

The correct solution is also done using such jetty-context.xml, but with another pattern. In a Spring application, we need to scan the Spring jars, and this alone will already give a massive boost if you have many dependencies. Even better is if you only scan the spring-web jars instead. If you have Spring Security, then it might also be needed to include those jars.

As such, the pattern that gave me maximum speedup is shown here:

<?xml version="1.0"?>
<!DOCTYPE Configure PUBLIC "-//Jetty//Configure//EN" "http://www.eclipse.org/jetty/configure_9_0.dtd">

<Configure class="org.eclipse.jetty.webapp.WebAppContext">

<Call name="setAttribute">
<Arg>org.eclipse.jetty.server.webapp.WebInfIncludeJarPattern</Arg>
<Arg>.*/spring-security[^/]*\.jar$|.*/spring-web[^/]*\.jar$|.*/classes/.*</Arg>
</Call>

</Configure>

We exclude anything that is not in our classes folder in WEB-INF, as well as any jars that do not include the regex pattern given.

Hope this helps someone!

• There's also the quickstart module in Jetty 9.2.x that can do the scan at build/compile time, which creates a jetty-quickstart.xml of what it finds in the war file, making the production startup sub-second. – Joakim Erdfelt Nov 14 '14 at 11:58
• That's pretty cool actually. I'll try to find an example of how to do that, so I can add it to this answer, or you can submit your own if you have one in an answer :). Thanks! – froginvasion Nov 15 '14 at 11:09
• I don't see any big difference regardless which solution I tried. – Vadim Ferderer Jun 19 '15 at 16:07
• Are you sure the jetty-context is being used? If so, try tweaking the regular expression, there might be other big libraries that cause the delay. – froginvasion Jul 8 '15 at 9:39
• If using Gradle instead of Maven, I could successfully apply this configuration using the Gretty plugin and setting the jetty-env configuration parameter . – Juan Calero May 24 '16 at 8:50


text:
# Naive Set Theory by Halmos is confusing to a layman like me

I want to be able to express set notations fluently in math fields used in machine learning, so I started reading Naive Set Theory by Halmos.

But I have been facing a lot of problems like :

1. On pages 1-6 , I encountered if and only if and had to go to Wikipedia, to actually understand it .
2. Also , I had to search Math.SE to understand such sentences as :
• It is equally harmless if the letter used has already been used with "for some" or "for all". Recall that "for some $x \ (x \in A)$" means the same as "for some $y \ (y \in A)$" ; it follows that a judicious change of notation will always avert alphabetic collisions.

• " nothing contains everything "

Every page is a conundrum that requires huge amounts of mental gymnastics. I think I'm not ready to read the book, yet.

Can anyone recommend a better introduction to informal set theory than Halmos ?

My Background : I majored in biology and attended calculus, statistics, real analysis, and linear algebra classes in a university. However, I dropped out of all math classes very early to focus on biology. Now, I want to learn math again. The high school didn't teach any theoretical foundation of math at all.

• You can try with : Derek Goldrei, Classic set theory (1996), but some "practice" with mathematical and logic symbolism is needed ... – Mauro ALLEGRANZA Apr 23 '15 at 15:00
• You could start with the first two chapters of Discrete Mathematics by Rosen. – Al Jebr Apr 23 '15 at 15:03
• may I suggest, as a somewhat soft introduction, David Velleman's How To Prove It? – essay Apr 23 '15 at 15:14
• Please note that "set notation" is quite different from set theory. While every mathematician is familiar with the former, a lot less are familiar with the latter, which is concerned with the theoretical foundations of the concept of set. I am not familiar with machine learning, but I doubt that it requires set theory. You might be better off studying some of the mathematics actually involved in machine learning, like statistics. – A.P. Apr 23 '15 at 15:55
• "If and only if" is completely standard mathematical terminology. I'm extremely surprised you never came across it before given that you've taken courses in, e.g., real analysis. – David Richerby Apr 23 '15 at 21:05

You are ready. You don't read math book like you read a novel. You can literally spend days on one page. You are not going to find a better book than Halmos's book; so you might as well grab a ton of scratch paper and go to town.

I do recommend that you get acquainted with the fundamentals of logic and boolean algebra first. You must become comfortable with implies, if and only if, for all, there exists, and, and or.

In terms of set theory, the phrase 'nothing contains everything' out of context, can be taken to mean either that the empty set contains all sets or that there is no such thing as the set of everything.

The first interpretation is ridiculous. The second is actually quite profound and has not always been believed.

Finally, there is something an old boss of mine once told me. "Nobody ever accomplished anything by reading the whole book." There is much in Halmos that you probably just don't need to know. Don't feel obliged to learn everything in the book.

• Go back to your old boss, and tell him that if you read the whole book, you accomplish "reading the entire thing". Which you cannot possibly accomplish otherwise. :-D – Asaf Karagila Apr 23 '15 at 23:21
• But that's not how internet arguments work, @StevenGregory. – Nit Apr 24 '15 at 0:11
• Does 'how to prove it' by velleman teach all I need to know? – crocket Apr 24 '15 at 3:37
• @Minsky It will certainly get you up to speed on the basics of logic. – steven gregory Apr 24 '15 at 4:06
• It has been said that everything on the internet that is said without a smiley face at the end will be taken seriously. I see now that even things with a smiley face at the end are taken seriously. (I was one of the first people to vote this answer, and I do agree with what you wrote there. Don't get me wrong about that. I never told anyone to read an entire book, if anything it's using something for reference, or reading several books.) – Asaf Karagila Apr 24 '15 at 14:36

I want to be able to express set notations fluently in math fields used in machine learning.

A book on set theory probably isn't the right place to be looking. Here's my advice:

1. Start off by trying to understand "propositional logic" (aka "boolean logic".) Start by Googling terms like "introduction to propositional logic." Perhaps get yourself a good introductory book on logic. Following sylvia's advice, consider getting your hands on How To Prove It and/or similar books.

2. Once you understand propositional logic, make it your goal to understand "first-order logic." Try googling "introduction to first-order logic" and/or similar search terms.

3. Seriously, make sure you understand first-order logic. Being able to express one's ideas correctly using first-order logic is arguably one of the most important skills a mathematician must possess.

4. Realize that you don't have to use set-builder notation to express yourself unambiguously. In particular, observe that the following both express the same thing.

• $A = \{x \in X \mid \mathrm{blah}\}$.

• $A$ is the unique subset of $X$ such that (for all $x \in X$) the following are equivalent.

• $x \in A$

• $\mathrm{blah}$

• Does 'how to prove it' by velleman teach all I need to know? – crocket Apr 24 '15 at 3:37
• @Minsky , it is quite a nice little book - especially for beginners ; it helps you get nicely primed and ready for Proofs , First-Order Logic , Set Theory , Functions etc. After that , I would suggest you to pick up Rosen -- wonderful book with lots of problems :) Happy 'Math'ing :) – pranav Apr 24 '15 at 4:29
• Your phrasing in point 4 is very convoluted. Why not just say that "Let $X$ be the subset of $A$ containing exactly those elements that blah"? – David Richerby Apr 24 '15 at 6:46
• @pranav How is discrete mathematics going to help me with my journey toward machine learning algorithms? Does it help me understand 'naive set theory' better? – crocket Apr 24 '15 at 8:01
• Hi , @Minsky , discrete math is going to teach you logic , set theory , functions , a spattering of number theory , combinatorics , graphs , trees , automata theory , primarily . Amongst these , the most useful for ML would be Set Theory , functions , Combinatorics , Graph Theory and Trees . You will gain an insight into how to use principles like Pigeonhole Principle without any fuss . All this stuff , you will encounter while studying ML , so better to be comfortable beforehand . Hope this helps :) Any further questions , I am happy to answer :) – pranav Apr 24 '15 at 8:05

I think Halmos' Naive Set Theory is primarily concerned with set theory as a foundation on top of which mathematics is built, but the word "naive", if I understand correctly, just means he's viewing the concept of a set concretely as a collection of things rather than axiomatically as being whatever satisfies the axioms. As to set theory applied to machine learning, it may be that what is needed differs from the content of Halmos' book. I like the book by E. Kamke, which was reprinted by Dover Books, but I don't know how well suited to machine learning the topic is. Is it useful in machine learning to know how to prove that $2^{\aleph_0}\ne\aleph_\omega$? I wouldn't be surprised if it's not, but I don't know.

As for the difference between "for some $x$, ($x\in A)$" and "for some $y$, $(y\in A)$", it is the same as the difference between the first and last terms in this expression: $$\sum_{x=1}^5 x^2 = \underbrace{1^2 + 2^2 + 3^2 +4^2 + 5^2}_{\text{No }x\text{ or }y\text{ appears here.}} = \sum_{y=1}^5 y^2. \tag 1$$ $x$ and $y$ are "bound" variables here. There is a Wikipedia article about this: http://en.wikipedia.org/wiki/Free_variables_and_bound_variables The first and last expressions in $(1)$ are called "alphabetic variants" of each other. If one is faced with an expression like $$\left(\sum_{i\in A}f(i)\right)\left(\sum_{i\in B} g(i)\right)$$ it can be useful to write this alphabetic variant: $$\left(\sum_{i\in A}f(i)\right)\left(\sum_{j\in B} g(j)\right)$$ because from that one can go on to see that this is equal to $$\sum_{i\in A}\left(\sum_{j\in B} \Big( f(i)g(j) \Big) \right).$$ A similar thing happens when one wants to put formulas in first-order logic into what is called prenex normal form.

I would take "nothing contains everything" to mean that there is no set of which everything is a member. In particular, in the conventional Zermelo–Fraenkel theory, no set is a member of itself. Moreover, every set has more subsets than it has members, so its subsets cannot all be members of it, although in some instances some of them are. See in particular this article: http://en.wikipedia.org/wiki/Cantor%27s_theorem

While not exactly an introduction to set theory per se I considered An Introduction to Proofs and the Mathematical Vernacular by Martin V. Day to be of great help in getting acquainted with a number of concepts and notations.
Although it's focus lies on reading, writing and checking proofs it provides all the necessary information to understand all those proofs. In my opinion it manages to keep the language simple and aids students to find their way by pointing out important caveats.

I think you're reading the wrong book. Of course, if you want to continue reading Halmos for fun and/or the intellectual challenge, that's great, but what you're doing is the equivalent of trying to learn to drive by reading books about automotive engineering. A more mathematical analogy would be to think back to the courses you took on calculus and real analysis: the calculus course was about how to use differentiation and integration to solve problems, whereas the analysis course is about how differentiation and integration work "under the hood".

For machine learning, you will be a user of sets and you might do some calculation on sets but you won't be doing research into what sets are and what are the limits of what they can do. For your purposes, you don't really need to know what's "under the hood" and it will be entirely sufficient to say that a set is a collection of objects defined by some stated property. Yes, that way lies Russell's paradox but Russell's paradox only comes up if you use "weird" properties to define sets and you won't be going anywhere like that. In particular, essentially all the objects you'll come across that you might want to describe as "sets" will be subsets of something that definitely is a set, such as the integers. In those areas, set theory works in just the way you'd expect it to.

The first chapter of any undergrad textbook on general discrete mathematics will almost certainly contain all the set theory you need for machine learning.

• Yes, that weird property of $x=x$ or $x\text{ has a single element}$... – Asaf Karagila Apr 24 '15 at 7:16
• @AsafKaragila But users of sets almost always have an implicit universal set in mind. There's nothing set-theoretically weird about "$x$ is an integer and $x=x$" or "$X$ is a set of vertices of my graph and $X$ has a single element." – David Richerby Apr 24 '15 at 7:46
• So you're essentially taking more than you claim to have taken. You're using the fact that the integers are a set, or that your graph has a power set, and the availability of separation (or bounded comprehension). This is more than you claim in your answer, and the difference is exactly where understanding Russell's paradox. I'm not advocating for the OP to sit and plow through Jech and Kunen, or even through all of Halmos' book. I'm only pointing out that "those weird properties" might not be so weird, and that you need to understand a bit more than the minimal use, in order to make good use. – Asaf Karagila Apr 24 '15 at 8:05
• Yes, I'm assuming all of those things. Just like everybody who uses mathematics just assumes that the real numbers exist and have the obvious properties. As a computer scientist, almost every collection of objects I deal with is finite; almost all of the rest are countable and pretty much all the rest are finite unions of real intervals. So, yes, I can just assume that everything I want to call a set is a set and has all the expected properties. – David Richerby Apr 24 '15 at 8:32
• One possible hiccup here is that machine learning involves a lot of probability so might involve some measure theory. I can imagine that that would require some actual set theory. – David Richerby Apr 24 '15 at 8:34


text:
# emptyPolyhedron -- generates the empty polyhedron in n-space

## Synopsis

• Usage:
P = emptyPolyhedron n
• Inputs:
• Outputs:

## Description

Generates the empty polyhedron in n-space.

 i1 : P = emptyPolyhedron 3 o1 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => -1 number of facets => 0 number of rays => 0 number of vertices => 0 o1 : Polyhedron

## Ways to use emptyPolyhedron :

• "emptyPolyhedron(ZZ)"

## For the programmer

The object emptyPolyhedron is .