Theory of Numbers, Math 116
MWF, 8:00-9:05 AM, Room S2 206.
Office hours: M-W from 9:05 to 11:35 AM, or by
appointment.
Complete Syllabus
Solutions to odd numbered problems (this is more complete than the solutions in the back of the book)
IMPORTANT:
If you want to learn your grades so far, and how
your scores are compared with the rest of the class please log into
Blackboard here.
Material covered in class:
08-24: Divisibility. The division algorithm.
08-26:
More division algorithm, numbers 'of the form... '. Representation
of numbers using various bases, how to transform a number written
in one base to another.
08-28: Furlough day, no classes.
08-31: Binary to hexadecimal (and vice-versa) 'trick'. Prime numbers and ideas/facts on their distribution.
09-02: Divisibility Criteria.
09-04: Furlough day, no classes.
09-07: Labor day, no classes.
09-09: gcd and the Euclidean algorithm.
09-11: Applications of gcd and the Euclidean algorithm.
09-14: The fundamental theorem of arithmentic. Polinomials with integral coefficients have roots in Z or not in Q
09-16: Squares, non-squares, square-free numbers.
09-18: Linear Diophantine equations.
09-21: Congruences modulo m. Remainders revisited.
09-23: CSR mod m.
09-25: Furlough day, no classes.
09-28: Congruence equations.
09-30: Chinese Remainder Theorem.
10-02: Proofs of things skipped before.
10-05: Proofs of things skipped before.
10-07: Review. Bring questions.
10-09: Exam 1 (all the info you need is here)
10-12: Wilson's theorem.
10-14: Fermat's Little Theorem.
10-16: Aside on Z_n. Euler phi-function.
10-19: Euler's theorem.
10-21: Multiplicative functions, phi is multiplicative, the handout with this proof is here NEW!!!!
10-23: Solving equations involving phi.
10-26: The sum of divisors and number of divisors functions.
10-28: Perfect, deficient, and abundant numbers
10-30: Mobius function, intro to Mobius inversion formula.
11-02: Mobius inversion formula proof, examples.
11-04: Review.
11-06: Exam 2.
11-09: Order modulo n of an integer.
11-13: Primitive roots modulo n.
11-16: RRS's and orders of elements
11-18: Finding all primitive roots.
11-20: Primitive roots of powers of primes.
Quizzes, Solutions,
Handouts, etc. (pdf files)... and a few links.
Problems assigned from the book and quiz info Updated
11/11
Assignment 1
Solved Problems 1
Fibonachos? (link)
Binary Sudoku (link)
Assignment 1 Solutions
The primes pages (link)
What's special about this number? (link)
Number Gossip (link)
Great Internet Mersenne Prime Search (link)
Assignment 3
Quiz 2 Solutions
Solved Problems 2
36 Methods of mathematical proof (link)
POP Mathematics (link)
Math in The Simpsons (link) and Math in Futurama (link)
Assignment 3 Solutions
Assignment 5
Quiz 4 Solutions
Solved Problems 3
Exam 1 Cheat Sheet
Assignment 5 Solutions
Exam 1 Solutions
Assignment 6
Solved Problems 4
Assignment 6 Solutions
Exam 2 Cheat Sheet
Quiz 7 Solutions
Exam 2 Solutions
Solved Problems 5
Final Exam Spring '09
Quiz 8 Solutions
NEW!!!!
Final Exam Info
NEW!!!!
Final Exam Cheat Sheet
NEW!!!!
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