Summer 2022 - MATH 342 D100
Elementary Number Theory (3)
Class Number: 3772
Delivery Method: In Person
Course Times + Location:
Mo 2:30 PM – 4:20 PM
SWH 10041, Burnaby
We 2:30 PM – 3:20 PM
SWH 10041, Burnaby
Exam Times + Location:
Aug 10, 2022
12:00 PM – 3:00 PM
AQ 3181, Burnaby
1 778 782-3339
Prerequisites:MATH 240 or 232, with a minimum grade of C-, and one additional 200 level MATH or MACM course.
The prime numbers, unique factorization, congruences and quadratic reciprocity. Topics include the RSA public key cryptosystem and the prime number theorem. Quantitative.
- Numbers and Sequences, Divisibility, Prime Numbers, Dirichlet's Theorem.
- Greatest Common Divisors, The Euclidean Algorithm, Continued Fraction Expansions, Linear Diophantine Equations.
- The Fundamental Theorem of Arithmetic.
- Introduction to Congruences, Linear Congruences, The Chinese Remainder Theorem, Solving Polynomial Congruences.
- Systems of Linear Congruences, The Distribution of Primes.
- Wilson's Theorem and Fermat's Little Theorem, Euler's Theorem, Pseudoprimes.
- The Euler Phi-Function, The Sum and Number of Divisors, Moebius Inversion, Perfect Numbers and Mersenne Primes.
- Integer factorization methods, primality testing, RSA public key crypto system.
- The Order of an Integer and Primitive Roots, Primitive Roots for Primes, Index Arithmetic, The Existence of Primitive Roots.
- Quadratic Residues and Nonresidues, The Law of Quadratic Reciprocity, The Jacobi Symbol.
- Sums of Squares, Pythagorean Triples, Infinite Descent, Pell's Equation.
- Additional topics and applications.
- Assignments 30%
- Quizzes 10%
- Midterm 20%
- Final Exam 40%
THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Elementary Number Theory and Its Applications. Kenneth Rosen. 6th Edition; 2011 Pearson.
E-Text available via VitalSource
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