CMPS/MATH 2170 Discrete Mathematics
Fall 13
Slides, pictures
Monday 8/26/13:
Propositional logic slides,
series_parallel_circuits,
Wednesday 8/28/13:
Logical equivalences table,
implication,
contrapositive_inverse_converse,
propositionalEquivalences,
propositionalEquivalencesEx,
propositionalEquivalencesEx2,
constructNewEquivalencesFromOthers,
constructNewEquivalencesFromOthers2,
Friday 8/30/13:
Boolean_functions,
onlyIf,
Boolean_functions2,
countingBooleanFunctions,
logicGates,
functionalCompleteness,
functionalCompleteness2,
constructFullDNF_from_truthTable,
functionalCompleteness3,
circuit,
Wednesday 9/4/13:
predicatesQuantifiers,
propositionalFunction,
propositionalFunctionEx,
universalQuantifier,
universalQuantifierEx,
sets,
universalQuantifierEx2,
existentialQuantifier,
existentialQuantifierEx,
quantifiers_true_false,
negatingQuantifiedExpressions,
negatingQuantifiedExpressionsEx,
negatingQuantifiedExpressionsEx2,
specifyingDomains,
Friday 9/6/13:
universalQuantifier,
existentialQuantifier,
examples1,
squareRoot,
squareRoot-comment,
nestedQuantifiers-trueFalseTable,
negatingNestedQuantifiers,
examples2,
examples3,
Monday 9/9/13:
language,
firstOrder_language,
sentences_and_subsets,
Wednesday 9/11/13:
ProofTable
proofs-terminology,
directProof,
indirectProof_byContrapositive,
indirectProofEx,
indirectProofEx2,
proofOfEquivalence,
truthTable,
proofByContradiction,
proofByContradiction2,
proofOfEquivalence-Justification,
Friday 9/13/13:
proofByCases,
proofByCases2,
proofByCases3,
proofByContradiction,
existenceProof-constructive,
existenceProof-nonConstructive,
counterExamples,
Monday 9/16/13:
sets,
n-tuple,
setBuilderNotation,
commonlyUsedSets,
equality_and_subset,
Venn_diagram_examples,
cardinality_and_emptySet,
Cartesian_product,
powerSet,
cardinalityPowerSet_proof1,
cardinalityPowerSet_proof2,
Wednesday 9/18/13:
Set identities table,
setOperations,
deMorgans_for_sets,
bigCup_bigCap,
functions,
domain_codomain,
image_range,
xi,
Friday 9/20/13:
homework2,
injective_surjective_bijective,
functionsEx1,
truthTable,
functionsEx2,
functionsEx3,
inverse,
inverse2,
composition,
Monday 9/23/13:
floor_ceiling,
sequence,
geometric_and_arithmetic_progressions,
summations_and_indexSubstitution,
geometricSeries,
geometricSeries2,
arithmeticSeries_and_cardinality,
cardinality_and_countableSets,
Wednesday 9/25/13:
oddPositiveIntegers_countable,
oddPositiveIntegers_countable2,
oddPositiveIntegers_countable3,
oddPositiveIntegers_countable4,
integers_countable,
integers_countable2,
positiveRationalNumbers_countable,
positiveRationalNumbers_countable2,
realNumbers_uncountable,
realNumbers_uncountable2,
Friday 9/27/13:
induction,
inductionProofRecipe,
geometricSeries_inductiveProof,
geometricSeries_inductiveProof2,
arithmeticSeries_inductiveProof,
arithmeticSeries_inductiveProof2,
squareTilingTheorem,
squareTilingTheoremEx,
squareTilingTheorem_proofIdea,
Monday 9/30/13:
factorial,
induction_factorial,
induction_set_deMorgan,
induction_set_deMorgan2,
induction_set_deMorgan3,
weak_and_strong_induction,
strongInduction_productPrimes,
strongInduction_productPrimes2,
Wednesday 10/2/13:
triangulation slides
backwardReasoning,
forwardReasoning,
wrongProofUsingBackwardReasoning,
test1,
recursiveDefinitions,
theoremFibonacciNumbers,
Friday 10/4/13:
factorial_and_Power_2,
towersOfHanoi,
towers_recursiveFormula1,
towers_recursiveFormula2,
towersExample,
towersExample2,
expandRecurrence,
towersInduction,
recursivelyDefinedSets,
wellFormedArithmeticFormulae,
Monday 10/7/13:
wfaf,
wfafTheorem,
compute_power_of_3,
compute_power_of_3_recursive_squaring,
recursiveSquaring_runtime,
expandRecurrence,
Monday 10/14/13:
expandRecurrence_proveInduction,
expandExample,
inductionExample,
test1,
recursiveDefinitions,
recursiveDefinitionsGraph,
Wednesday 10/16/13:
divides,
divides_Theorem,
divides_TheoremEx,
divisionAlgorithm,
divisionAlgorithmEx,
congruence,
congruence-Ex-congruenceClass,
Zm,
Friday 10/18/13:
Zm,
Zm_properties,
Zm_properties2,
prime,
primeFactor_sqrt,
fundamentalThmArithmetic,
proof1,
proof2,
Monday 10/21/13:
commutative_nonAssociative,
infinitelyManyPrimes,
gcd,
relativelyPrime,
inverse_modulo_m,
Euclidean_algorithm,
Euclidean_algorithm2,
Euclidean_algorithmEx,
Wednesday 10/23/13:
inverse_modulo_m,
inverseExistenceTheorem,
linearCongruence,
linearCongruenceEx,
cryptography,
public_key_cryptosystem,
RSA,
RSA2,
Friday 10/25/13:
public_key_cryptosystem,
RSA,
RSA-Theorem,
RSA_primeFactorization,
Fermats_little_theorem,
lemma,
RSA-Theorem-proof,
Monday 10/28/13:
counting-ex1,
unionRules,
additionPrinciple,
multiplicationRule,
ex4,
ex5-a-b,
ex5-c-d,
10-1-ex5-d-1,
ex5-d-3,
ex6-bitstrings,
ex7-functions,
ex7-functions-oneToOne,
Wednesday 10/30/13:
countFunctions,
pigeonHole1,
pigeonHole2,
pigeonHole2Proof,
pigeonHole2_ex,
permutations,
combinations,
Friday 11/1/13:
combinations,
committeeEx,
cardHandsEx,
bitSequences,
combinationsWithRepetitions,
hotDogEx2,
permutationsCombinationsOverviewTable,
binomialTheorem,
pascalsTriangle,
pascalsIdentity,
Monday 11/4/13:
testAnnouncement,
binomialTheorem,
PascalsTriangle,
proofBinomialTheorem,
proofPascalsIdentity,
proofBinomialTheoremEx,
probability,
sixSidedDie,
uniformProbability,
loadedDie,
pokerHands,
Wednesday 11/6/13:
diceSummingTo7,
lotteryProbability,
propertiesProbabilities,
conditionalProbability,
flipThreeCoinsEx,
boysGirlsEx,
Friday 11/8/13:
BernoulliTrial,
BernoulliTrial2,
binomialDistribution,
randomVariable1,
randomVariable2,
expectedValue,
rollDieExpectedValue,
Monday 11/11/13:
testTopics,
expectedValue,
rollingOneDie,
rollingTwoDice,
rollingTwoDice2,
linearityOfExpectation,
rollingTwoDice3,
Wednesday 11/13/13:
Probability distributions slides
expectation-linearity-and-product,
expectedValueBinomialDistribution,
varianceMotivation,
varianceDef_and_Ex,
Monday 11/18/13:
relationDef,
relationEx,
sqrt,
relationOnA,
relationOnA_Ex,
propertiesOfRelations,
n-ary-Relation,
equivalenceRelation,
Wednesday 11/20/13:
countingRoads,
equivalenceRelation,
equivalenceRelationEx,
equivalenceRelation_proof,
equivalenceClass,
equivalenceClasses_disjoint,
Friday 11/22/13:
undirectedGraph,
directedGraph,
graphVariants,
adjacency,
adjacencyMatrix,
adjacencyLists,
Monday 11/25/13:
Graph slides,
adjacencyLists_degrees,
storageComplexityAdjacencyLists,
pathExamples,
acyclicGraph_tree,
forest,
DAG,
thm_tree_vertices_edges,
thm_tree_vertices_edges2,
Monday 12/1/13:
finalExam,
tree_depth_height,
depth_height_Ex,
tree_vertex_terminologies,
definitions_types_of_trees,
leaves_in_k-ary_tree,
leaves_in_k-ary_tree2,
completeBinaryTree,
Wednesday 12/4/13:
completeTreeEx,
leavesCompleteTree,
verticesCompleteBinaryTree,
binaryTree_height_vertices,
planarGraph,
K33_nonPlanar,
Friday 12/6/13:
nonPlanar-graphs,
EulersFormula,
proof1,
proof2,
proof3,
Last modified by Carola Wenk,
cwenk -at- tulane -dot- edu,
