Summer 2023 - MATH 342 D100
Elementary Number Theory (3)
Class Number: 2193
Delivery Method: In Person
Course Times + Location:
May 8 – Aug 4, 2023: Mon, 2:30–4:20 p.m.
May 8 – Aug 4, 2023: Wed, 2:30–3:20 p.m.
Exam Times + Location:
Aug 14, 2023
Mon, 8:30–11:30 a.m.
1 778 782-3339
1 778 782-3337
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 10%
- Quizzes 10%
- Midterm 20%
- Final Exam 60%
THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks. Please pay careful attention to the options discussed in class at the beginning of the semester.
Elementary Number Theory and Its Applications. Kenneth Rosen. 6th Edition; 2011 Pearson.
E-Text available via VitalSource
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