Spring 2018 MATH 115 001 LEC

Introduction to Number Theory
Schedule: 
SectionDays/TimesLocationInstructorClass
001 LECMoWeFr 11:00AM - 11:59AMEvans 9Alexander B Givental26647
UnitsEnrollment Status
4Open
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SectionDays/TimesLocationInstructorClass
101 DIS12:00AM - 12:00AM  31572
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Prerequisites: 53 and 54, but the expected level of mathematical maturity is at leasta as high as in math 113.   

Description: This is the first time I teach number theory, and so I tried to select a text from among all those recommended by our experts who taught it before. Of course, I failed: Most of the texts turned out to be too long and focusing on too many boring details, some others didn't contain the material I wanted to cover. Finally I ended up with choosing the text  http://poincare.matf.bg.ac.rs/~zarkom/Book_Math_TheoryOfNumbers_ABaker.pdf , which is only 90 pages long, but covers all the desired imaterial (and a bit more) with complete and straightforward proofs. It is based on a quarter-long introductory course at Cambridge (UK) intended for all brands of future mathematicians. Yet, the book is very unusual, as it looks more like a research survey written in mid-19th century. It shows how seemingly diverse aspects of classical number theory could have come out of a natural line of quest by a single person, apparently Gauss.  It is hard to read, because each sentence requires some thinking, and each page asks for comments, as it often neglects to elucidate the underlying ideas and possible connections with other topics. So, the course is going to become an intensive exercise in group reading of a truly mathematical text, in the process of which we will attempt to uncover all the hidden ideas and connections - which is what understanding  a subject should mean.         

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