### Course Calendar

• The section numbers below correspond to those in the course notes. See the topic list below the calendar for the corresponding section numbers in Rosen.
• The midterm dates on the calendar are subject to change. You will be given plenty of advance notice, if they do.
• As we get a feel for how much material we can cover in one lecture, I'll start to fill in squares for future classes, in case you want to read ahead.
MondayWednesdayFriday
Jan 1 - Jan 5 First day of class
Introduction, overview
Review: Notation, Induction
Begin §3: Divisibility
Jan 8 - Jan 12 Finish §3: Divisibility
§4: Representations of Integers
Finish §4
§5: The GCD
Finish §5
§6: The Euclidean Algorithm
Jan 15 - Jan 19 Finish §6
§7: Prime Numbers
§8: The Fundamental Theorem of Arithmetic Finish §8
Start §9: The LCM
Jan 22 - Jan 26 Finish §9: The LCM §10: Primes of the Form 4k + 3
§12: Irrational Numbers
§11: Diophantine Equations
Jan 29 - Feb 2 §13: Congruences (Introduction) §13: Congruences (Modular Arithmetic) §14, § 18:Applications of Congruences
Feb 5 - Feb 9 Finish §18 §15: The Congruence Method
§16: Linear Congruences in One Variable
Finish §16
Feb 12 - Feb 16 NO CLASS Review MIDTERM 1
Feb 19 - Feb 23 NO CLASS NO CLASS NO CLASS
Feb 26 - Mar 2 §17: The Chinese Remainder Theorem Finish §17
§19: Wilson's Theorem
§20: Fermat's Little Theorem
Finish §20
§21: Pseudoprimes
Mar 5 - Mar 9 §22: The Euler phi-function Finish §22
§23: Arithmetic Functions
Finish §23
§24: Formulas for some Arithmetic Functions
Mar 12 - Mar 16 §25: Perfect Numbers and Mersenne Primes §26: Primitive Roots Finish §26
Mar 19 - Mar 23 §27: Primitive Roots for Primes Review MIDTERM 2
Mar 26 - Mar 30 §28: Index Arithmetic and Discrete Logarithms Intro to Cryptography NO CLASS
Apr 2 - Apr 6 NO CLASS Crypto Final exam information and review
April 19, 3:30pm: Final Exam

### Course outline

We will cover the following sections of the textbook, not necessarily in this order. Deviations from this plan may be necessary.
• 1.3. Induction
• 1.5. Divisibility
• 2.1. Representations of integers
• 3.1. Prime numbers
• 3.2. The distribution of primes (only the statement of the Prime Number Theorem)
• 3.3. Greatest common divisors
• 3.4. The Euclidean algorithm
• 3.5. The fundamental theorem of arithmetic
• 3.6. Fermat Factorization only
• 3.7. Linear Diophantine equations
• 4.1. Introduction to congruences
• 4.2. Linear congruences
• 4.3. The Chinese Remainder Theorem
• 5.1. Divisibility tests
• 6.1. Wilson's Theorem and Fermat's Little Theorem
• 6.2. Pseudoprimes
• 6.3. Euler's Theorem
• 7.1. The Euler phi-function
• 7.2. The sum and number of divisors
• 7.3. Perfect numbers and Mersenne primes
• 8.1. Character ciphers
• 8.3. Exponentiation ciphers
• 8.4. Public key cryptography
• 9.1. The order of an integer and primitive roots
• 9.2. Primitive roots for primes
• 9.3. The existence of primitive roots
• 9.4. Discrete logarithms and index arithmetic
Depending on time availability we will also cover some of the following topics:
• 5.5. Check digits (ISBN code only)
• 8.6. Cryptographic protocols and applications (digital signatures only)
• 10.2 The ElGamal cryptosystem.
• 11.1 Quadratic residues and nonresidues
• 11.2 The Law of Quadratic reciprocity
• 11.1 The Jacobi Symbol
• 13.1 Pythagorean Triples
• 13.2 Fermat's Last Theorem (case n=4 only)