Course Calendar

Please note:

• 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.

	Monday	Wednesday	Friday
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)