Applied Combinatorics

Basic Information

  • Course: Math 3012, Applied Combinatorics
  • Time: MWF 9:00am-10:00am
  • Instructor: Jun Lu
    • Email: jlu39@math.gatech.edu
    • Office: Skiles 225A
  • Textbook: Discrete and Combinatorial Mathematics(Fifth Edition) by Grimaldi
  • Office Hour: WF 10am-11am

Grading

  • Homework. Homework is assigned and collected weekly. Each homework contains 15 problems. You need to complete the first 10 problems and only 5 of them will be graded. Only one homework is graded every two weeks. The last five problems are candidates for tests. You can and are encouraged to work on the homework with your classmates, but the homework you hand in should be written by yourself. No late homework will be accepted. Each homework is worth 3%(7 in total)
  • Quizzes. Four quizzes will be given in lectures to check the attendance, worth 10% in total
  • Test. Three 50-minute tests will be given in lectures. Each test contains 6 problems and 3 of them are directedly drawn from homework. No books, notes, calculators are allowed during the test. Each test is worth 15%
  • Final. The final is comprehensive, worth 20%
  • Project. There will be a final project which involves some computer programming. You can choose any programming language you like. It is worth 4%
  • The final grade will be curved

Regrading

Any regrading request should be submitted to the lecturer within no more than one week after the tests have been returned in class.

Make-ups

Make-up test is allowed only in emergency situations and I must be notified prior to the exam. You need also provide a reasonable, written confirmation of your absence.

Academic Dishonesty

All students are expected to comply with the Georgia Tech Honor Code. Any evidence of cheating or other violations of the Georgia Tech Honor Code will be submitted directly to the Dean of Students. Cheating includes, but is not limited to: using a calculator, books, or any form of notes on tests; copying directly from any source, including friends, classmates, tutors, or solutions manuals; allowing another person to copy your work.

Tentative Schedule

Basic Utilities

  • Week 1: Mathematical Induction
  • Week 2: Recursions and Generating Functions
  • Week 3: Number Theory

Counting

  • Week 4: Test 1, Permutations and Combinations
  • Week 5: Binomial Theorem, Combination Identities
  • Week 6: Catalan Number and Principle of Inclusion and Exclusion
  • Week 7: Functions and Pigeonhole Principle
  • Week 8: Probability Theory and Its Applications

Graph Theory

  • Week 9: Test 2, Introduction to Graph Theory
  • Week 10: Trees
  • Week 11: Planar Graph, Hamiltonian Path and Cycle
  • Week 12: Test 3, Graph Algorithms

Homework and Tests