This course is a gentle introduction to Number Theory, and at the same time can serve to motivate the contsructions and theorems that you will encounter in Algebraic Structures in Years 2 and 3.
Number Theory is one of the most ancient topics in mathematics, and an interdisciplinary one: in its advanced phase it combines algebra, geometry and analysis.
Topics to be covered:
- Rationals and irrationals
- Divisibility, primes, unique factorization
- Congruences
- Quadratic reciprocity
- Arithmetic functions
- Examples of diophantine equations
- Farey sequences, continued fractions and Pell's equation
- The distribution of primes
We shall follow, more or less, the book by Niven and Zuckerman "An Introduction to the Theory of Numbers". There are copies in the math library and it is also available on the web. The Fifth Edition (with Montogomery as a co-author) contains a lot of material, more than we can cover in class. You are welcome to consult it.
There will be 12 HW assignments. You have to submit 10 out of 12 to get full credit.
See you on Monday,
Udi
Number Theory is one of the most ancient topics in mathematics, and an interdisciplinary one: in its advanced phase it combines algebra, geometry and analysis.
Topics to be covered:
- Rationals and irrationals
- Divisibility, primes, unique factorization
- Congruences
- Quadratic reciprocity
- Arithmetic functions
- Examples of diophantine equations
- Farey sequences, continued fractions and Pell's equation
- The distribution of primes
We shall follow, more or less, the book by Niven and Zuckerman "An Introduction to the Theory of Numbers". There are copies in the math library and it is also available on the web. The Fifth Edition (with Montogomery as a co-author) contains a lot of material, more than we can cover in class. You are welcome to consult it.
There will be 12 HW assignments. You have to submit 10 out of 12 to get full credit.
See you on Monday,
Udi
- Teacher: אהוד דה-שליט
- TA: גיא ספיר