MAT 312/ AMS 351 (Applied Algebra) - Fall 2017

Time and Place : TuTh 11:30-12:50; Mathematics P131

Instructor : Radu Laza

Office : Math Tower 4-121
Email :  radu.laza@stonybrook.edu

Office Hours: Thr 1:30-2:30, Thr 4-6

TA: Mu Zhao

Overview

This course covers the fundamentals of abstract algebra: groups, informal set theory, relations, polynomials, together with some applications: error correcting codes, Burnside's theorem, computational complexity, Chinese remainder theorem. This course is offered as both AMS 351 and MAT 312.

Textbook

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Grading


Schedule

WeekTopicSections CoveredHW Assigments
(1) Aug 29, 31 Division Algorithm & gcd
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Induction
1.1
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1.2
(2) Sept 7 Primes and Unique Factorization 1.3 HW1 (due Sept 14)
(3) Sept 12, 14 Congruence classes
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Solving linear congruences
1.4
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1.5
HW2 (due Sept 21)
(4) Sept 19, 21 Euler's Theorem
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Review (Chapter 1)
1.6 HW3 (due Sept 28)
(5) Sept 26, 28 Midterm 1: Tuesday, Sept 26 (in class)
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Permutations (1)
Chapter 1 (Number theory)
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4.1
(6) Oct 3, 5 Permutations (2)
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Intro to Groups
4.2
4.3
HW4 (due Oct 12)
(7) Oct 10, 12 Algebraic Structures 4.4 HW5 (due Oct 19)
(8) Oct 17, 19 Groups and Codes 5.1
5.2
HW6 (due Oct 26)
(9) Oct 24, 26 Groups 5.2
5.3
HW7
(10) Oct 31, Nov 2 Groups
Review
Ch. 5
(11) Nov 7, 9 Midterm 2: Tuesday, Nov 7 (in class)
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Group and Codes
Ch. 4, 5.1--5.3
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5.4
HW8 (due Nov 16)
(12) Nov 14, 16 Polynomials 5.4
6.1, 6.2
(13) Nov 21 Factorization 6.3 HW9 (due Nov 28)
(14) Nov 28, 30 Polynomial congruence classes
Cyclic Codes
6.4
6.5
HW10 (due Dec 5)
(15) Dec 5, 7
Review
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Final Exam
HW11* (due Dec 7)