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  Syllabus Mat 2155 Foundations for Advanced Mathematics

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 Catalog Description. MATH 2155. Foundations for Advanced Mathematics (3-0-3) Prerequisite: MATH 1132. Topics include fundamentals of logic, techniques of proof, sets and relations, well ordering and mathematical induction, and functions.

Text: A transition to Advanced Mathematics, Smith, Eggen, St. Andre, Brooks Cole, 4th Edition, ISBN: 0-534-34028-8

Syllabus for MATH 2155

Foundations for Advanced Mathematics  

CHAPTER         1        Logic and Proofs
                            1.1     Propositions and Connectives 1
                            1.2     Conditionals and Biconditionals 9
                            1.3     Quantifiers 18
                            1.4     Mathematical Proofs 26
                            1.5     Proofs Involving Quantifiers 40
                            1.6     Additional Examples of Proofs 49

CHAPTER          2        Set Theory
                            2.1     Basic Notions of Set Theory 59
                             2.2       Set Operations 67
                            2.3     Extended Set Operations and indexed Families of Sets 74
                            2.4     Induction 85
                            2.5     Equivalent Forms of Induction 97
2.6          Principles of Counting 104
 
CHAPTER          3        Relations
                            3.1     Cartesian Products and Relations115
                            3.2     Equivalence Relations 129
                            3.3     Partitions 136
                            3.4     Ordering Relations 141
                            3.5     Graphs of Relations 151
 
CHAPTER          4        Functions
                            4.1     Functions as Relations 161
                            4.2     Constructions of Functions 171
                            4.3     Functions That Are Onto; One-to-One Functions 179
                            4.4     Induced Set Functions
                           
CHAPTER          5        Cardinality
                            5.1     Equivalent Sets; Finite Sets 195
                            5.2     Infinite Sets 203
                            5.3     Countable Sets 209
                            5.4     The Ordering of Cardinal Numbers 218
 

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