Elementary Number Theory (MATH 317)

2021 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
6.00 / 6.00 ECTS (for students admitted in the 2013-14 Academic Year or following years)
Mohammad Sadek mmsadek@sabanciuniv.edu,
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English
Undergraduate
MATH102 MATH201
Formal lecture
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CONTENT

Divisibility, prime numbers, congruences, quadratic residues, arithmetic functions, the Riemann Zeta function.

OBJECTIVE

Refer to the course content

LEARNING OUTCOME

Prove simple facts about divisibility, greatest common divisors, least common multiples,
Understand the Euclidean Algorithm
Understand the Fundamental Theorem of Arithmetic
Solve linear Diophantine equations and linear congruences
Understand and apply Fermat's Little Theorem
Determine Euler Phi Function and prove simple facts about Euler Phi Function
Prove simple facts about primitive roots
Apply the Law of Quadratic Reciprocity
Show simple facts about quadratic residues
Decide if an integer can be written as a Sum of Squares
Apply standard proof methods like mathematical induction, direct and indirect proofs

Present simple proofs in a precise and formally correct way.

ASSESSMENT METHODS and CRITERIA

  Percentage (%)
Final 30
Midterm 50
Exam 20

RECOMENDED or REQUIRED READINGS

Textbook

A Friendly Introduction to Number Theory
by
Joseph H. Silverman