Nov 22, 2024  
2014-2015 Undergraduate Academic Catalog 
    
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2014-2015 Undergraduate Academic Catalog [ARCHIVED CATALOG]

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MA 183 - Transition to Advanced Topics in Mathematics

3 lecture hours 0 lab hours 3 credits
Course Description
This course provides an introduction to proof techniques to be used in upper level mathematics courses. Topics include logic and proofs, set theory, relations and partitions, functions, and cardinality of sets.
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
• Be proficient in elementary logic, including using truth tables to prove logical equivalence
• manipulate logical sentences symbolically and semantically-for example, apply DeMorgan’s Law to construct denials
• Be familiar with the natural numbers, integers, rational numbers, real numbers, and complex numbers
• Be proficient in interpreting and manipulating existential and universal quantifiers
• read and construct proofs using direct and indirect methods; choose methods appropriately
• read and construct proofs involving quantifiers
• Be proficient in set theory including construction of sets, subsets, power sets, complements, unions, intersections, and products
• interpret unions and intersections of indexed families of sets
• read and construct proofs involving set theoretic concepts
• apply the Principle of Mathematical Induction and equivalent forms
• manipulate summations in sigma notation
• read and construct proofs related to relations, equivalence relations, and partitions of sets
• Be familiar with functions as relations; injections, surjections, and bijections
• construct functions from other functions-for example, compositions, restrictions, and extensions
• read and construct proofs related to functions
• Be familiar with cardinality for finite, countable, and uncountable sets
Prerequisites by Topic
• None
Course Topics
• Elementary logic with truth tables
• Quantifiers
• Methods of proof
• Set Theory
• Operations with sets including indexed families of sets
• Principle of Mathematical Induction and equivalent forms
• Cartesian products
• Relations, equivalence relations, and partitions of sets
• Functions, Surjections, Injections
• Cardinality of sets including countable sets
Coordinator
Anthony van Groningen


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