AMS 301 FINITE MATHEMATICAL STRUCTURES

Spring 2019

Class Time and Place: TuTh 1:00 - 2:20 pm, ESS 001
Instructor: Prof. Alan Tucker
Offices: Eng 127 (back right office)
Office Hours: Tu 11:30-12:50 pm , Wed 11 am - 12:30 pm, and F 10am - noon or by appointment
How to Reach Prof. Tucker: telephone: 2-9941; e-mail: alan.tucker@stonybrook.edu
Course Text: Applied Combinatorics, Sixth Edition, by A.Tucker, John Wiley & Sons.
Tests: three hour Tests (31%,31%,23%), the last one during final exam week.
Homework: Assigned weekly and submitted through Blackboard; graded out of a maximum score of 5; Counts for 15% of course grade; Solutions to all problems available before tests.
Weekly Assignments Listed Below.

Graders Unless otherwise noted, office hours are in the AMS Help Room in Harriman 132.
> Yuhao.Liu.1@stonybrook.edu, office hours: M 4-6 pm, grading A-F
Baiyu.Chen@stonybrook.edu, office hours: Fr 8:40-10:40 am, grading G-Le
Xinyue.Dong@stonybrook.edu, office hours: Tues 4-6 pm, grading Li-Pa
Skylar.Holst@stonybrook.edu, office hours: MW 1-2pm, grading Pe-V
Andrew.Chen.5@stonybrook.edu, office hours: M 9-11 am, Grading W-Z
Students with disabilities or who need special assistance with exams or other aspects of the course are asked to let Prof. Tucker know about their circumstances at the beginning of the course.
Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Any suspected instance of academic dishonesty will be reported to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http: //www.stonybrook.edu/uaa/academicjudiciary
Critical Incident Management: Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of University Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the school of Medicine are required to follow their school-specific procedures. Further information about most academic matters can be found in the Undergraduate Bulletin, the Undergraduate Class Schedule, and the Faculty-Employee Handbook.
Mastermind Extra Credit:In the first month of the course, there will be weekly Mastermind puzzles posted on this webpage each Thursday night at 10:00 pm. Mastermind is explained in the Prelude at the front of the textbook. The first five students to email the correct solution (with an explanation of their reasoning) will get 3 extra points on the first test; the next five students to e-mail me the correct sequence will get 2 extra points on the first test and the next 5 students will get one extra point on the first test.

Learning Outcomes for AMS 301
1.) Strengthen logical reasoning skills to solve combinatorial problems using:
        * elements of propositional calculus;
        * proof by contradiction;
        * logical consequences of assumptions.
2.) Learn to find multiple (equally valid) ways to solve a combinatorics problem
        * apply a top-down strategy (breaking a problem into parts and subparts)
        * apply a bottom-up strategy (solving special subcases and building up).
        * learn to solve problems from first principles, rather than looking for existing templates or formulas.
        * solve a complementary problem;
        * use different strategies to categorize subcases of a problem;
3.) Learn basic graph theory results and apply them in problem-solving: 
        * isomorphism; 
        * planar graphs; 
        * Hamilton circuits and Euler cycles;
        * graph coloring; 
        * trees and ways to search them.
4.) Use formulas for counting basic combinatorial outcomes to construct solutions to more complex combinatorial enumeration problems:
        * permutations, with and without repetition;
        * combinations, with and without repetition.
5.) Apply counting strategies to solve discrete probability problems.
6.) Use specialized techniques to solve combinatorial enumeration problems:
        * generating functions; 
        * recurrence relations; 
        * inclusion-exclusion principle.

COURSE OUTLINE:
NOTE THAT PROBLEMS ARE FROM THE SIXTH EDITION OF THE TEXTBOOK. THE NUMBERING AND WORDING OF MANY PROBLEMS IS DIFFERENT IN EARLIER EDITIONS. See Corrections of 6th and 5th editions of Applied Combinatorics for errors in the text and errors in Odd-Numbered Answers. Week 1 -- Jan 29-31: Graph Theory Basics, Isomorphism-- Section 1.1,1.2,1.3 Homework1(due 2/5): Sect 1.1: 3,6,9,15,18,20,22,23; Sect. 1.2: 5adh,6cfh,7; Sect. 1.3: 1c,2bc,6,10, 12a. Week 2 -- Feb 5-7: Planar Graphs, Euler Cycles-- Section 1.4, 2.1 Homework2(due 2/12) Sect. 1.4: 3ad,7cdfgh,9,11,15,23,25; Sect. 2.1: 2,3,7,16 Week 3 -- Feb12-14: Hamilton Circuits, Graph Coloring--Section 2.2, 2.3, 2.4 Homework3(due 2/19): Sect. 2.2: 4ehlm,7b,9,16; Sect 2.3: 1bfjm, 14,16; Sect 2.4: 7a. Third Mastermind puzzle. There are two solutions (no credit for one solution). Send solutions with brief explanation to Yuhao.Liu.1@stonybrook.edu R W R Bk Score: 1 white Bk Y G R Score: 2 white R G Bu W Score: 1 black, 1 white G R R G Score: 1 black, 1 white Bu Bk W Y Score: 1 black, 1 white Week 4 -- Feb 19-21: Trees and Searching-- Section 3.1 Homkwork4:(due 2/26): Sect. 3.1: 1a,2,4,6,10,13,14,25,29; Sect 3.2: 1ab,4,5,16b,19. Week 5 -- Feb 26-28: Traveling Salesperson Problem--Section 3.3 Homework OPTIONAL (for your own practice): Sect 3.3: 1,5 Week 6 -- Mar 5-7: Review and First Test (Mar 7) Fall 18 First Test Spring 18 First Test Fall 17 First Test Solutions to Old First Tests Solutions to Homeworks Week 7 -- Mar 12-14: Basic Permutations and Combinations-- Section 5.1, 2 Homework5(due 3/26): Sect.5.1: 7,9,10,13,14,16ab,18,24,26,29,32,33; Sect 5.2: 4,7,9,14,16bce,22,29,48,53,69a SPRING BREAK Mar 18-22 Week 8 -- Mar 26-28: Counting Problems with Repetition-- Sections 5.3,5.4, Homework6(due 4/2): Sect 5.1: 25,30,36; Sect 5.2: 34,40,55; Sect 5.3: 1,4,6,8,9,12,20; Sect 5.4: 1,3ac,9,11,14,27 Week 9- Apr 2-4: Generating Function Models-- Section 6.1,6.4 Homework7(due 4/9): Sect 5.2: 25,46 56; Sect 5.3: 15,19,22; Sect. 5.4: 10,18,21,28,48,49; Sect 6.1: 2a,4ad,6,8; Sect 6.4:1,2,3 Week 10 --Apr 9-11:Evaluating Generating Function Coefficients-- Section 6.2, 6.4 Homework8(4/16): Sect 6.1: 3bd,7,13,16; Sect 6.2: 1,3,7,11bc,18a,20,22; Sect 6.4: 6,7a Week 11-- Apr 16-18: Review and Test 2 (Test Apr 18) Old Second Tests Solutions to Old Second Tests Solutions to Homeworks Week 12-- Apr 23-25: Recurrence Relations-- Section 7.1, 7.3 Homework9(due 4/30): Sect. 7.1: 2,6ab,7,10,12,16a,20, 28, 30; 7.3:1,2,3a Week 13-- Apr 30-May 2: Inclusion-Exclusion Principle-- Section 8.1, 8.2 Homework 10:(due 5/7): Sect. 8.1: 8,10,13,14,15,16,20,22,29,36; Sect. 8.2: 2,3,6,11,12,15,19,23a,32 Week 14-- May 7-9: Rook Polynomials and Review for third test-- section 8.3 Homework11:due:5/8-put under door of Phys A137): 8.2: 31,34; 8.3: 2a, 4, 5. Finals Week-- THIRD TEST IS HELD AT THE ASSIGNED TIME FOR THE FINAL EXAM, Tues May 21st, 2:30-3:30 (just one hour); Old Third Tests Solutions Old Third Tests Solutions to Homeworks
Historical Curve in Prof. Tucker's AMS 301 classes:
approximately 25% A's, 40% B's, 25% C's, 10% D's,F's & W's