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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/

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

Simple Logic Tutorial: (Logic Cafť) 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 (Tarskiís world)

Tarskiís 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/

Boolean Algebra

http://plato.stanford.edu/entries/boolalg-math/

http://www.play-hookey.com/digital/boolean_algebra.html

GCD and LCM: http://www.purplemath.com/modules/lcm_gcf.htm

 Paradox:  http://www.cut-the-knot.com/selfreference/russell.html

http://www.treasure-troves.com/bios/RussellBertrand.html

http://Plato.stanford.edu/entries/russell-paradox

4

Number Theory and Methods of Proof

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

5

Induction and Recursion

 Induction: http://whyslopes.com/etc/ThreeSkillsForAlgebra/ch04.html

http://www.thiel.edu/mathproject/atps/CHPTR05/P028.HTM

http://www.purplemath.com/modules/inductn.htm

Towers of Hanoi:

http://eluzions.com/Puzzles/Java/Hanoi/ or http://www.ypass.net/crap/java/toh/

http://www.lawrencehallofscience.org/Java/Tower/tower.html

http://www.cut-the-knot.org/recurrence/hanoi.shtml

http://www.pbs.org/teachersource/mathline/concepts/historyandmathematics/activity3.shtm

Recursion: ( chaos and fractals)

http://mathforum.org/library/topics/chaos/

http://mathforum.org/library/topics/fractals/

http://www.shodor.org/interactivate/lessons/frac3.html ( chaos game)

http://www.shodor.org/interactivate/lessons/frac1.html

 

6

Counting and Probability

Cards: http://www.cs4fn.org/mathemagic/magicshuffles/

Computers 4 Fun http://www.cs4fn.org/

Monty Hall: http://www.grand-illusions.com/simulator/montysim.htm

Pascalís Triangle: http://ptri1.tripod.com/

http://mathforum.org/library/topics/combinatorics/

Permutations and Combinations:

http://faculty.sjcny.edu/~fritz/MAT203/Permutations.htm

7

Functions

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

http://www.shodor.org/interactivate/activities/fm/index.html ( function machine) 

http://www.shodor.org/interactivate/lessons/fm2.html

http://www.coolmath.com/func1.htm ( basic)

http://archives.math.utk.edu/visual.calculus/0/functions.11/index.html 

 

8

Relations

  http://regentsprep.org/Regents/mathb/7A1/relationdefinition.htm

9

Graphs and Trees

http://mathforum.org/library/topics/graph_theory/

 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/

http://www.mathforamerica.org/

 http://mathforum.org/library/topics/

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

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

http://www.microworlds.com/library/math/

http://mathforum.org/library/topics/computer_science/

http://www.sheppardsoftware.com/mathbb1.htm

http://www.thiel.edu/academics/math/UsflLnk/Default.htm 

 

 

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)