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MAT 203 MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE

CATALOGUE DESCRIPTION:

The emphasis will be on algorithmic problem solving and discrete mathematical concepts including logic, sets, Boolean algebra, relations, functions, induction and recursion, counting principles and combinatorics, graphs, and trees. Use of the computer as a problem solving

tool will be integrated with theory. Fundamental algorithms including sorting, searching, and tree traversal will be introduced.

Prerequisite: MAT 113 or equivalent. 4 hours a week, 1 semester, 4 credits.

TEXT: Susanna Epp, Discrete Mathematics with Applications, Third Edition, Cengage Learning, Belmont, CA, 2004.

Website: http://condor.depaul.edu/~sepp/DMappletsEtc.htm

 

Topics

Readings and Links

1

Logic and Validity

http://logik.phl.univie.ac.at/~chris/formular-uk-zentral.html

http://faculty.sjcny.edu/~fritz/MAT203/logiccalc.html

Truth table constructor : http://sciris.shu.edu/~borowski/Truth/

Truth  table practice: http://www.math.csusb.edu/notes/quizzes/tablequiz/tablepractice.html

Simple Logic Tutorial: (Logic Café) http://www.oakland.edu/phil/cafe/

Logic circuits: http://math.hws.edu/TMCM/java/xLogicCircuits/index.html

Circuit builder: http://www.jhu.edu/~virtlab/logic/log_cir.htm

                          http://www.jhu.edu/~virtlab/logic/logic.htm

Logic Quiz: http://logic.tamu.edu/cgi-bin/quizmaster

Conditionals: http://www.sjsu.edu/depts/itl/7/part2/f-wk5b.html

2

Predicate Calculus

http://www.bu.edu/linguistics/UG/course/lx502-s04/local/tarski.html (Java)

http://www-rohan.sdsu.edu/~ituba/block/index.html (Tarski’s world)

Tarski’s World: http://www.inf.ethz.ch/~staerk/tarski/ (old)

3

Set Theory

 http://www.geocities.com/basicmathsets/

http://infinity.sequoias.cc.ca.us/faculty/woodbury/Stats/Tutorial/Sets_Venn2.htm

http://www.stat.sc.edu/~west/applets/Venn.html

http://wblrd.sk.ca/~mathb30cs/prob/les2/notes.html

http://wblrd.sk.ca/~mathb30cs/prob/les2/assign.html

http://www.shodor.org/interactivate/activities/vdiagram/#

http://www.rwc.uc.edu/koehler/comath/java/venn.html

Cantor Sets http://www.mathacademy.com/pr/prime/articles/cantset/

4

Number Theory and Methods of Proof

 http://www.cut-the-knot.org/proofs/index.shtml

5

Induction and Recursion

 

6

Counting and Probability

Pascal’s Triangle: http://ptri1.tripod.com/

 

7

Functions

 Infinity http://www.hectorparr.freeuk.com/hcp/infinity.htm

8

Relations

 

9

Graphs and Trees

 Kruskal algorithm: http://students.ceid.upatras.gr/~papagel/project/kruskal.htm

 

 10

Finite State Automata

 

 

Problem Solving and

Critical Thinking

 http://www.sjsu.edu/depts/itl/

 

 Other Resources

http://www.cut-the-knot.org

 http://www.cut-the-knot.org/collection.shtml

http://www.venndiagram.com/

http://mathforum.org/mathtools/cell.html?co=m5&tp=7.15&id=372&new_co=dm

http://en2.wikipedia.org/wiki/Mathematics

http://www.mathacademy.com/pr/minitext/infinity/

http://www.hotmath.com/

 

Mathematical Games

http://shell.cas.usf.edu/~mccolm/RGintro.html (Games Mathematicians Play)

http://www.sjsu.edu/depts/itl/7/active/index.html (Logic Games)

http://www.shyamsundergupta.com/  (Number Recreations)