MATH-UA.120: Discrete Mathematics Fall 2011

This is a past class.

[[!table header="no" class="mointable" data=""" Class Time/Location | Tuesday, Thursday 11:00am-12:50pm, 7 East 12th Street, Room 123 Instructor | Andreas Kloeckner Email | kloeckner@cims.nyu.edu Office | Courant Institute, Warren Weaver Hall, Room 1105A Office Hours | Monday, Wednesday 4pm-5pm Class Webpage | http://wiki.tiker.net/Teaching/DiscreteMathFall2011 Email Listserv | http://lists.tiker.net/listinfo/discretefall11, discretefall11@tiker.net, archive """]]

[[!toc ]]

Topics and goals

Our major goal will be to familiarize ourselves with some of the important tools of discrete mathematics.

  • Mathematical language, logic, writing, and proof
  • Set theory
  • Functions and Relations
  • Combinatorics and discrete probability
  • Graph theory and trees

Text

Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games, by Douglas E. Ensley and J. Winston Crawley. Wiley, ISBN 0-471-47602-1

The book has a rather helpful companion web site which we will be using on occasion.

Assessment

[[!inline pages="/Assessment" quick="yes" raw="yes"]]

Material about Tests

[[!map pages="^Teaching/DiscreteMathFall2011/Quiz[0-9]+.*"]]

Homework

[[!map pages="^Teaching/DiscreteMathFall2011/HomeworkSet[0-9]+"]]

/HomeworkSolutions

Tentative Calendar

[[!table header="no" class="mointable" data=""" Week | Day | Book Section | Topic/Notes 1 | 9/6 | 1.1 | First Examples 9/8 | 1.2 | Number Puzzles and Sequences 2 | 9/13 | 1.3 | Truth-tellers, Liars, and Propositional Logic 9/15 | 1.4 | Predicates 3 | 9/20 | 1.5 | Quiz; Implications 9/22 | 2.1 | Mathematical Writing 4 | 9/27 | 2.2 | Proofs about Numbers 9/29 | 2.3 | Mathematical Induction 5 | 10/4 | 2.5 | Contradiction and the Pigeonhole Principle (taught by Matthew Elsey) 10/6 | 3.1, 3.2 | Set Definitions and Operations (taught by Matthew Elsey) 6 | 10/11 | Fall Break (no class) || 10/13 | Review || 7 | 10/18 | Midterm 1 on 1.1-2.5 || 10/20 | 3.3 | Proving Set Properties 8 | 10/25 | 3.4 | Boolean Algebra 10/27 | 4.1 | Definitions of Functions, Diagrams 9 | 11/1 | 4.2 | Quiz; Relations, Inverses, Composition 11/3 | 4.2 | Relations, Inverses, Composition cont'd 10 | 11/8 | 4.3 | Properties of Functions and Set Cardinality 11/10 | 4.4, 4.5 | Properties of Relations, Equivalence Relations 11 | 11/15 | Review || 11/17 | Midterm 2 on 2-4.5 || 12 | 11/22 | 5.1, 5.2 | Intro to Combinatorics, Basic Rules for Counting 11/24 | Thanksgiving Break (no class) || 13 | 11/29 | 5.3, 5.4 | Cominatorics and the Binomial Theorem, Binary Sequences 12/1 | 5.5 | Recursive Counting 14 | 12/6 | 6.1, 6.2 | Intro to Probability, Sum and Product Rules 12/8 | 6.3 | Quiz; Probability in Games of Chance 15 | 12/13 | 7.1, 7.2 | Graph Theory, Proofs about Graphs and Trees 12/15 | Review || 16 | 12/20 | Final Exam 10am-11:50am /!\ || """]]

(see also the academic calendar)