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Thursday, May 31, 2018

Advanced Knowledge Problem of the Week 5-31-18: Function with Bounded Derivative [Real Analysis]

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Solution below.

Tuesday, May 29, 2018

Problem of the Week 5-29-18: Numbers with Certain Divisors [Number Theory]

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Solution below.

Thursday, May 24, 2018

New Video Series on Complex Analysis

Interested in learning a bit more about complex variables and some theorems about them? Then check out this new video series covering some of the basics of complex analysis! Complex analysis is an immensely useful subject that is found in many branches of mathematics. The residue theorem is especially well known as being an extremely important method for the integration of functions (real or complex!). Some other topics discussed include complex differentiation, Cauchy's Integral Formula, Liouville's theorem, the Möbius transformation, and much more!


Advanced Knowledge Problem of the Week 5-24-18: A Metric Space [Topology]

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Solution below.

Monday, May 21, 2018

Problem of the Week 5-22-18: Integer Function [Number Theory]

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Solution below.

Thursday, May 17, 2018

Advanced Knowledge Problem of the Week 5-17-18: Alternating Group Generators [Group Theory]

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Solution below.

Tuesday, May 15, 2018

Problem of the Week 5-15-18: A Set of Integers [Number Theory]

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Solution below.

Thursday, May 10, 2018

Advanced Knowledge Problem of the Week 5-10-18: How many prime factors? [Number Theory]

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Solution below.

Tuesday, May 8, 2018

Some Notable Mathematicians/Teachers


Many mathematicians have been notable not just for their contributions to mathematics, but also for helping teach the next generation of mathematicians. A number of important mathematicians have tutored and helped other important mathematicians progress in their careers. Here are a few such mathematicians.

Paul ErdÅ‘s - Paul ErdÅ‘s was a notable mathematician who lived an eccentric and mathematically productive lifestyle. He was known for collaborating with many other mathematicians, so many that his collaborating spawned the concept of the ErdÅ‘s number, which measures how far away mathematicians are from citing some of ErdÅ‘s's work. ErdÅ‘s also influenced younger mathematicians, such as the Fields Medalist Terence Tao.

Ernst Kummer - Ernst Kummer was a notable mathematician who made important contributions to mathematics in fields such as geometry and number theory. He also helped educate people in mathematics, one example being that he trained german officers in ballistics. He also was the advisor of several notable students and helped inspire Leopold Kronecker to pursue a career in mathematics.

David Hilbert - David Hilbert was a very prominent mathematician who created the list of Hilbert's problems; a list of 23 unsolved (at the time) and important problems in mathematics. Hilbert helped make the University of Göttingen a leading institution in mathematics. Hilbert also had many doctoral students; at the University of Göttingen Hilbert had 69 doctoral students.

George Pólya - George Pólya was another prominent Hungarian mathematician like Paul ErdÅ‘s. He wrote numerous books about problem solving, which served to help many students problem solve in mathematics. One of his more popular books, How to Solve It, has sold more than one million copies and discusses strategies for approaching/solving problems.

Monday, May 7, 2018

Problem of the Week 5-8-18: Sum of Digits [Number Theory]

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Solution below.

Thursday, May 3, 2018

Advanced Knowledge Problem of the Week 5-3-18: A Lack of Primitive Roots [Number Theory]

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Solution below.

Tuesday, May 1, 2018

Problem of the Week 5-1-18: Problem on Primality [Number Theory]

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Solution below.