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# Class Notes at Carnegie Mellon University

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### Exam Study Guides for CARNEGIE-MELLON Courses

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##### 21127 Lecture 17: rec17

Concepts of Math: Recitation 17 October 26, 2015 Midterm 2 Review Important: the quality of explanation matters more than quantity of problems solved. 1. Please see Midterm 2 Practice problems, posted on Irinas Blackboard ...

Mathematical Sciences
21127
Brendan Sullivan
##### 21238 Lecture Notes - Lecture 1: Topological Vector Space, Free Module, Module Homomorphism

Math Studies Algebra II Prof. Clinton Conley Spring 2017 Contents 1 January 18, 2017 4 1.1 Logistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4. . . . . . . . . . 1.2 Modules . ....

Mathematical Sciences
21238
Clinton Conley
##### 21127 Lecture Notes - Lecture 2: Quadratic Formula, Natural Number, Additive Identity

Mathematical Sciences
21127
Brendan Sullivan
##### 21127 Lecture Notes - Lecture 4: Mathematical Game, Natural Number, Determinacy

Mathematical Sciences
21127
Brendan Sullivan
##### 21127 Lecture Notes - Lecture 5: Domino Tiling, Subset, Natural Number

Lecture521127ConceptsofMath09.07.2012 Administrivia Homework1willbereturnedonTuesday,inrecitation. Homework2hasbeenposted,andisduenextThursday,inrecitation. InductionWrapup Letssummarizesomeofourworkoninductivearguments,ex...

Mathematical Sciences
21127
Brendan Sullivan
##### 21127 Lecture Notes - Lecture 6: Empty Set, Subset, Burh

Mathematical Sciences
21127
Brendan Sullivan
##### 21127 Lecture Notes - Lecture 7: Die Tageszeitung

Lecture721127ConceptsofMath09.12.2012 PowerSets(continued) Anotherexample.UseA=f?;f1;?gg.Then P(A)=f?;f?g;ff1;?gg;f?;f1;?ggg Itistrue,inthisexample,that ?2A;f?gA;f?g2P(A);f?gP(A) WhatdoesP(N)looklike?Letswritedownsomeexamp...

Mathematical Sciences
21127
Brendan Sullivan
##### 21127 Lecture Notes - Lecture 8: Mathematically Correct, Natural Number, Xsan

Lecture821127ConceptsofMath09.14.2012 SetsProofs Letsactuallywriteupsomerigorous,mathematicallycorrect,andwellwrittenproofs.AlloftheProposi tionscontainedhereareusefulfactsthatwecancitelateron,andwewouldexpectyoutobeableto...

Mathematical Sciences
21127
Brendan Sullivan
##### 21127 Lecture Notes - Lecture 9: Mathematical Induction, Prut, Eni

Mathematical Sciences
21127
Brendan Sullivan
##### 21127 Lecture Notes - Lecture 10: Natural Number, Logical Connective, Burh

Mathematical Sciences
21127
Brendan Sullivan
##### 21127 Lecture Notes - Lecture 11: European Route E6, Contraposition, Exclusive Economic Zone

Lecture1121127ConceptsofMath09.21.2012 BiconditionalStatementsandLogicalEquivalence Thephraseifandonlyifmeansexactlythat:ifandonlyif. PifQclearlymeansIfQthenP,i.e.Q)P. PonlyifQmeansItcannotbethecasethatPholdsandQfails.That...

Mathematical Sciences
21127
Brendan Sullivan
##### 21127 Lecture Notes - Lecture 12: Contraposition, Logical Biconditional, Rational Number

Lecture1221127ConceptsofMath09.24.2012 ImplementingProofStrategies Hereareseveralmoreexamplesofgood,wellwrittenproofsthatproperlyimplementthestrategieswewent overonFriday. LinearDiophantineEquations Proposition.Thereisnoin...

Mathematical Sciences
21127
Brendan Sullivan
##### 21127 Lecture Notes - Lecture 13: Universal Quantification, Logical Biconditional, Contraposition

Mathematical Sciences
21127
Brendan Sullivan
##### 21127 Lecture Notes - Lecture 14: Babe, Dirham, Natural Number

Mathematical Sciences
21127
Brendan Sullivan
##### 21127 Lecture Notes - Lecture 15: Computer-Aided Technologies, Kaiaphas, Holda

Lecture1521127ConceptsofMath10.03.2012 GeneralInduction Examplefromhomework RecallProblem5fromHomework2:MoBrendans,MoProblems.ThatwasaGeneralInductionproblem! Claim:Withcurrencynotesofdenominaton3and7Brendans,wecandenitely...

Mathematical Sciences
21127
Brendan Sullivan
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