**Math 453 (Sections D13,D14 and X13,X14): Elementary Theory of Numbers**

**Fall 2013**

**Instructor:** Florin P. Boca

**Office:** 362 Altgeld Hall

**Phone:** (217) 244 - 9928

**E-mail:** fboca at illinois dot edu

**Lectures:** 143 AH, MWF 11:00-11:50 am (Sections D13,D14), respectively
347 AH, MWF 12:00-12:50 pm (Sections X13,X14).

**Office hours:** Monday 3-4 pm, Thursday 3-4 pm.

**Course description:** This is a **rigorous** mathematical course, providing a
basic introduction to the theory of numbers. Core topics will include divisibility,
primes and factorization, congruences, arithmetic functions, quadratic residues and quadratic reciprocity,
primitive roots and orders. Additional topics covered at the discretion of the instructor include sums of squares,
Diophantine equations, continued fractions, Farey fractions, recurrences, and applications to primality testing and cryptopgraphy.

Credit: 3 OR 4 hours. 4 hours of credit requires approval of the instructor and department with completion of additional work of substance.

This course satisfies the General Education Criteria in Fall 2013 for a UIUC Quant Reasoning II course.

**Official prerequisite:** MATH 241 or equivalent.

**Recommended prerequisite:**
Math 347 or an equivalent
class covering rigorous mathematical proofs, especially proofs by mathematical induction and proofs by contradiction.

**Textbook: ** **James K. Strayer, ****Elementary Number Theory,****Waveland Press, Inc.,
1994/2002.**

**Grading policy:** Comprehensive final exam: ** 40%**. Midterm exams: ** 45%**.
Homework and quizzes: ** 15%**.

**Homework and quiz policy:** There will be 14 HW assignments, distributed roughly one per week.
HW assignments **# 2k+1** will be collected and (randomly)
selected problems will be graded. HW assignments **# 2k**
will not be collected. Instead, a 15 minutes quiz with two problems
from that assignment will be given.

Only the best 12 (out of 14) scores will count. As a result HW extension or make-up quizzes will not be allowed.

**Midterm exams:** **Midterm 1** Fri Sep 27
**Midterm 2** Th Oct 24
**Midterm 3** Wed Dec 4;

**Final exam:**
**D13,D14**:
8:00-11:00 am Fri Dec 20, 143 AH;
**X13,X14**:
7:00-10:00 pm Tu Dec 17, 347 AH.

**Books, notes and calculators are not allowed for tests**
(exams or quizzes). Group work is allowed for homework. However, solutions are expected to be written independently.

**Useful information** (please read carefully)

Last modified: *May 15, 2014*