He was a student of Arnold Sommerfeld and Heinrich Tietze at the University of Munich , where he received his doctorate in 1939 .
Karl Apfelbacher was a German mathematician who served as minister for higher public education in Upper Bavaria - East .
Karl Apfelbacher was a mathematician of Arnold Sommerfeld and Heinrich Tietze at the University of Munich , where Karl Apfelbacher received Karl Apfelbacher 's doctorate in 1939 .
Karl Apfelbacher was a German mathematician who served as minister for higher public education in Upper Bavaria - East .