Discrete Math- Schneider

Syllabus for MAT 237/637 CMP 232-Gillet 305

MAT 237: Applications of Discrete Mathematics.

4 hours, 4 credits. Concepts and applications of graph theory, recurrence relations, linear programming, game theory, difference equations, matrices, combinatorics, statistical inference, probability. Problem solving using mathematical modeling. PREREQ: MAT 176. Note: Primarily for students planning to teach mathematics in a secondary school.

CMP 232: Elementary Discrete Structures and Applications to Computer Science.

4 hours, 4 credits. Sets, relations, and functions; propositional calculus, Boolean algebras, and combinatorial circuits, counting methods; proof techniques; analysis of algorithms; graphs and trees, puzzles; finite machines, sequential circuits, and recognizers. PREREQ: MAT 172 or placement by the Department of Mathematics and Computer Science or Departmental permission. Note: Students who receive a grade below B- in MAT 172 are strongly urged to speak to an adviser in the Department of Mathematics and Computer Science prior to registering for CMP 232.

MAT 637: Topics in Discrete Mathematics.

60 hours, 4 credits. Topics chosen from probability, combinatorics, decision making, game theory, graph theory, recurrence relations, linear programming, statistical inference. Problem solving using mathematical modeling. PREREQ: Two semesters of calculus.

Location: Gi 305 TTH 1:00- 2:40 PM

Instructor: Robert Schneider

Contact Info:

email: robert.schneider@lehman.cuny.edu
web page: comet.lehman.cuny.edu/schneider/
office hours: Tues,Thur 10:45-11:45; 3:45-4:15 + appt.- Gillet 200

Final:The Final Exam will be given Thursday May 26 from 1:30-3:30

Grad Student Projects -- pick one:

Euler and Hamiltonian Paths -- 10.5
Shortest Path Problem-- 10.6
Planar Graphs-- 10.7
Minimum Spanning Trees-- 11.5
Generalized Pigeon Hole Principle and Applications (understand advanced Applications) --- 6.2

Grading Policy:

Homework tests (20 minutes) 20%

Midterm - 30 %

Final: 40%

Homework- 10%

extra credit will be given for various projects and exceptional class comments

MAT237 Course Outcomes [assessed using the problems in the brackets]:

1. Perform numeric and symbolic computations (as part of departmental math objective A) [1-12]

2 State and apply mathematical definitions and theorems (E) [1,4,7,8, 9, 10, 11, 12]

3. Count by using combinatorial arguments (A,B,C) [3,4,6,7,8,9]

4. Analyze and prove identities and inequalities for discrete functions (B, G) [2,9]

5. Apply discrete mathematics to real-life problems (C) [3,9,12]

Math Major Outcomes incorporated into MAT237 [assessed using problems in the brackets]:

A. Perform numeric and symbolic computations [1-12]

B. Construct and apply symbolic and graphical representations of functions [1,4,6]

C. Model real-life problems mathematically [3,9,12]

E. State and apply mathematical definitions and theorems [1,3,6,7,8,9,10,11,12]

G. Construct and present a rigorous mathematical argument [2,9,10,11]

Materials, Resources and Accommodating Disabilities:

textbook(recommendend): Discrete Mathematics and its Applications 7th edition by Kenneth H. Rosen
will give web sites that cover a lot of material
will hand out problem sets to go over
if interested in scientific computing download Python environment using Anaconda

see the following web page to see how to get Eclipse and PyDev to create an environment

You will need to set up your Eclipse environment to use this Anaconda

Topics:

Sets and Set Operations:Ch2
https://en.wikipedia.org/wiki/Naive_set_theory#Specifying_sets
problem set number 1
truth tables and proving logical statements
Apply to set theory identities
pdf of Python code for sets
pdf of some Maple code for sets
Go over first part of problem set 1-- hand in on Thur-- possible quiz anytime

Makeup problems for first HW quiz

Functions Sequences and Summation:Ch 2
second problem set
Widipedia Article about functions
more than you might want to know about floor and ceiling
countable and uncountable sets
Induction and Recursion: Ch 5
Problem set 3
An easy intro to induction
Another intro
Counting Techniques: Ch 6
Binomial Theorem

Problem Set 4

First 6 Problems of problem set 5

Function Growth: Ch 3
Introduction to Graphs: Ch 10
Applications of Graphs
pdf outline of maple class presentation
Some resources on web to read
little synopsis of graph theory
short outline of how to use graph theory in Maple
10.1,10.2,10.3 of text
google it
Problem Set 6

Department of Mathematics and Computer Science, Lehman College, City University of New York