# MAT 312/ AMS 351 (Applied Algebra) - Spring 2021

Time and Place : MWF 11:45am-12:40pm; Earth&Space 131

Instructor : Mikhail Movshev

Office : Math Tower 4-109
Email :  mmovshev@math.stonybrook.edu

Office Hours: MWF 10:00-11:00

Office: Math Tower S-240A

Email: Giovanni.Passeri@stonybrook.edu

## 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

## Announcements

• The first midterm will take place in class on Friday, Feb 25 (in class). It will cover all Chapter 1 of the textbook ("Number Theory"). To prepare for the exam, please review HW1-3, and the sample midterm .

• The second midterm will take place in class on Friday, Apr 8. It will focus on groups (All of Chapter 4, and 5.1-5.3). See the sample questions for Midterm 2 (this is longer than the actual exam). Solutions to the sample exam.

• The final exam (Friday, May 13, 11:15am-1:45pm) will cover the material from Midterm 1, Midterm 2, and the Chapter 6 on polynomials. Here are holutions to a practice final.

• There will be 2 midterms and a final. We will have 11 homework assignments.

• The exams count for 75% of the final grade. The division is : 35% for the final and 20% for each midterm. The remaining 25% will be for the homework assignments.

• No late HWs, and no make-up exams. (There will an extra make-up HW in case you missed one HW assignment).

# Schedule

 Week Topic Sections Covered HW Assignments (1) Jan 24, 26,28 Division Algorithm & gcdInduction 1.11.2 (2) Jan31,Feb2,4 Primes and Unique Factorization 1.3 (#1 due Feb 7) 1.1: 1, 2, 5 1.2: 2, 7, 8, 11 1.3: 3, 6, 8. (3) Feb 7, 9,11 Congruence classesSolving linear congruences 1.41.5 (#2 due Feb 14) 1.4: 1, 3, 4, 5, 7 1.5: 1, 2, 3, 4, 5 (4) Feb 14, 16,18 Euler's TheoremReview (Chapter 1) 1.6 (#3 due Feb 21) 1.6: 1, 2, 3, 5, 6, 7, 12, 13 (5) Feb 21, 23,25 Permutations (1) 4.1 Midterm 1: Friday, Feb 25 (in class) Chapter 1(Number theory) (6)Feb 28, Mar 2,4 Permutations (2) Intro to Groups 4.24.3 (#4 due Mar 7) 4.1: 3, 4 4.2: 1, 2, 4, 6, 7, 10, 13 (7) Mar 7,9,11 Algebraic Structures 4.4 (#5 due Mar 21 ) 4.3: 1, 3, 4, 5, 8 4.4: 1, 4, 5, 8, 10, 13, 15 (8) Mar 14,16,18 Spring Recess (9) Mar 21,23,25 Groups and Codes 5.15.2 (# 6 due Mar 28) 5.1: 2, 3, 4, 7, 8, 9 (10) Mar 28,30 Apr1 Groups 5.25.3 (#7 due Apr 4) 5.2: 1, 3, 5 5.3: 1, 3, 4, 7, 9 (11) Apr 4,6,8 Group and Codes 5.4 (#8 due Apr 11) 5.4: 2, 3, 4, 5, 6, 7 Midterm 2: Friday, Apr 8 (in class) Ch. 4,Ch. 5.1-5.3 (12) Apr 11,13,15 Polynomials 5.46.1, 6.2 (#9 due Apr 18) 6.1: 1, 2, 3 6.2: 1, 2, 3 (13) Apr 18,20,22 Factorization 6.3 (#10 due Apr 25) 6.3: 3, 4, 5, 6 (14) Apr 25,27,29 Polynomial congruence classesCyclic Codes 6.46.5 (#11 due May2) 6.4: 1, 2, 3 (15) May2,4,6 Review

If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact the Student Accessibility Support Center, Stony Brook Union Suite 107, (631) 632-6748, or at sasc@stonybrook.edu. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and the Student Accessibility Support Center. For procedures and information go to the following website: https://ehs.stonybrook.edu//programs/fire-safety/emergency-evacuation/evacuation-guide-disabilities and search Fire Safety and Evacuation and Disabilities.

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