CMPS/MATH 2170 Discrete Mathematics
Fall 15
Slides, pictures
Monday 8/24/15:
Propositional Logic slides,
propositionEx,
serialAndParallelCircuits,
Wednesday 8/26/15:
Logical equivalences table,
truthTables,
propositionalEquivalences,
deMorgans_Ex,
deMorgans_XOR,
newEquivalences,
implications,
onlyIf,
Friday 8/28/15:
booleanFunctions,
truthTableBooleanFunctions,
numberOfBooleanFunctions,
truthTableBooleanFunctions,
precedences_logicGates,
functionallyComplete,
functionallyComplete2,
DNF_example,
Monday 8/31/15:
predicatesAndQuantifiers,
propFunctionEx,
universalQuantifier,
universalQuantEx,
existentialQuantifier,
quantifierTrueFalseTable,
negatingQuantifiedExpressions,
Wednesday 9/2/15:
negationEx,
quantifiersRestrictedDomains1,
quantifiersRestrictedDomains2,
nestedQuantifiers1,
nestedQuantifiers2,
nestedQuantifiers3,
Friday 9/4/15:
Rules of inference table,
rules of inference table for quantified statements,
rulesOfInference,
proofEx1,
proofEx2,
proofEx3,
Wednesday 9/9/15:
Proof table,
proof_theorem_terminology,
directProof_oddInteger,
directProofEx,
indirectProof,
indirectProofEx,
indirectProofEx2,
proofByContradiction,
proofByContradiction2,
Friday 9/11/15:
proofByContradiction,
proofByContradiction_truthTable,
proofByContrapositiveCompared,
proofOfEquivalence,
proofOfEquivalence_4_vs_3,
hypotheticalSyllogism,
proofByCases,
proofByCasesEx,
Monday 9/14/15:
rules of inference table for quantified statements,
constructiveExistenceProof,
nonConstructiveExistenceProof,
counterExample,
backwardReasoning,
forwardReasoning,
wrongProof,
Wednesday 9/16/15:
sets,
oftenUsedSets,
subsets,
powerSet,
powerSetProof,
cartesianProduct,
cardinality,
Friday 9/18/15:
Set identities table,
setOperations,
setOperationsEx,
operationsOnSequences,
operationsOnSequencesEx,
deMorgans,
Monday 9/21/15:
officeHours,
function,
image,
functionEx,
functionEx2,
injective_surjective_def,
injective_surjective,
injective_surjective_Ex,
injective_surjective_Ex2,
injective_surjective_Ex2b,
injective_surjective_Ex3,
Friday 9/25/15:
inverseEx,
compositionAndInverse,
compositionAndInverseEx,
inverse_composition_def,
floor_ceiling,
sequences,
geometricProgression,
Monday 9/28/15:
injectiveSurjective,
cardinality,
injection,
finiteSet,
countablyInfinite,
countable_uncountable,
Z,
2N,
subsetCountable,
unionCountable,
unionCountable2,
unionCountable3,
Q,
Q2,
Q3,
R,
R2,
R3,
cardinalities,
Wednesday 9/30/15:
sequence,
cardinalityFiniteSets,
cardinality,
countableSets,
Q+,
Q+2,
R,
R2,
Friday 10/2/15:
quiz,
induction,
forall,
ex1a,
ex1b,
ex2,
Monday 10/5/15:
sequences_and_series,
geometricSeriesInduction1,
geometricSeriesInduction2,
tilingGrid1,
tilingGrid2,
weak_and_strong_induction,
Wednesday 10/7/15:
divides_prime,
midterm,
weak_strong_induction,
strongInduction,
productPrimesInduction,
productPrimesInduction2,
productPrimesInductionEx,
fibonacciInduction,
fibonacciInduction2,
Friday 10/9/15:
programVerification,
factorial,
factorialLoopInvariant1,
factorialLoopInvariant2,
multiply,
multiplyLoopInvariant1,
multiplyLoopInvariant2,
wrongInduction1,
wrongInduction2,
Monday 10/12/15:
recursivelyDefinedFunctions,
recursivelyDefinedFunctionsEx,
recursivelyDefinedFunctionsEx2,
Fibonacci_induction1,
Fibonacci_induction2,
solvingLinearRecurrenceRelations,
recurrenceExamples,
characteristicEquation,
recurrenceTheorem,
recurrenceTheoremProof,
FibonacciExample,
FibonacciExample2,
Wednesday 10/14/15:
towersOfHanoi,
hanoiEx,
Hn,
hanoiRecursion,
expandRecurrence,
hanoiInduction,
solvingLinearRecurrences,
Monday 10/19/15:
Topics for Midterm,
setEquivalenceProof,
powerset,
induction,
hw4,
Wednesday 10/21/15:
divides,
dividesThm,
prime,
fundThmArithmetic,
proof_exist_unique,
infinitelyManyPrimes,
proof,
Friday 10/24/15:
gcd,
gcd_lcm,
divisionAlgorithm_div_mod,
divisionAlgorithm_div_modEx,
congruent,
congruent_and_mod_theorem,
Monday 10/26/15:
divisionAlgo_congruences,
congruenceThm,
Zm_properties1,
Zm_properties2,
commutativeRing_finiteField,
EuclideanAlgorithmLemma,
EuclideanAlgorithm,
EuclideanAlgorithmCode,
Wednesday 10/28/15:
midterm,
solveLinearCongruences,
inverseEx,
inverseTheorem,
solveCongruenceEx,
BezoutsTheorem,
findInverseEx,
Friday 10/30/15:
inverseExContinued,
publicKeyCryptography,
publicKeyCryptography2,
FermatsLittleTheorem,
RSA,
RSA_Ex,
RSA2,
Monday 11/2/15:
RSA3,
lemma_chinese_remainder,
RSA_encryptionEx,
RSA_encryptionEx2,
RSA_encryptionEx3,
digitalSignatures,
encryption_vs_signatures,
Wednesday 11/4/15:
solveRecurrenceFibEx,
counting,
union_addition,
multiplicationEx,
multiplication,
wordCountEx1,
wordCountEx2,
Friday 11/6/15:
sumOfSquares,
pigeonHole_permutations_combinations,
permutations_combinations_Ex,
pigeonHoleEx,
Monday 11/9/15:
countBitSequences,
combinationsWithRepetitions,
cards_functions_Ex,
injectiveFunctions,
permutationsCombinationsTable,
BinomialTheorem,
PascalsIdentity,
Wednesday 11/11/15:
discreteProbability,
diceEx_fairDie,
uniformProbability,
diceEx_loadedDie,
lottery,
sumFairDice,
fourOfAKind,
fullHouse,
Friday 11/13/15:
Fixed RSA example,
propertiesOfProbabilities,
randomVariable,
flipCoin_heads,
flipCoin_game,
expectedValue,
expectedValueGameEx,
expectedValue_DieEx,
linearityOfExpectation,
Monday 11/16/15:
Probability slides
variance,
BernoulliTrial,
binomialDistributionExpectation,
Wednesday 11/18/15:
conditionalProbability,
independence,
ex1,
ex2,
BayesThm,
BayesEx,
BayesEx2,
BayesProof,
Friday 11/20/15:
relations,
relationsEx,
relation_nAry_onA,
propertiesOfRelationsOnA,
relationOnA_Ex,
equivalenceRelation,
equivalenceClass,
graphs,
graphExamples,
Monday 11/23/15:
graphs,
graphExamples,
adjMatrix_adjLists,
adjacent_degree,
handshakingLemma,
paths,
forest,
tree,
pathEx,
Monday 11/30/15:
graphTreeEx,
treeInduction1,
treeInduction2,
incident_leaf,
rootedTree,
kAryTree,
kAryTreeInduction,
Wednesday 12/2/15:
Topics for Final,
final,
full_kAry_tree_lemma,
complete_kAry_tree_lemma,
completeBinaryTreeLemma,
completeGraphs,
bipartiteGraph,
K4_planarGraph,
Last modified by Carola Wenk,
cwenk -at- tulane -dot- edu,
