Apr 20, 2024  
2021-2022 Undergraduate Academic Catalog 
    
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2021-2022 Undergraduate Academic Catalog [ARCHIVED CATALOG]

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MA 1830 - Transition to Advanced Topics in Mathematics

4 lecture hours 0 lab hours 4 credits
Course Description
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. (prereq: only open to AS students)
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
  • Demonstrate proficiency 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
  • Demonstrate familiarity with the natural numbers, integers, rational numbers, real numbers, and complex numbers
  • Demonstrate proficiency in interpreting and manipulating existential and universal quantifiers
  • Read and construct proofs using direct and indirect methods
  • Choose methods of proof appropriately
  • Read and construct proofs involving quantifiers
  • Demonstrate proficiency in elementary set theory including construction of sets, subsets, power sets, complements, unions, intersections, and Cartesian 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 its equivalent forms
  • Manipulate summations in sigma notation
  • Read and construct proofs related to relations, equivalence relations, and partitions of sets
  • Demonstrate familiarity 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
  • Demonstrate familiarity with cardinality for finite, countable, and uncountable sets
Prerequisites by Topic
  • None
Course Topics
  • Elementary logic with truth tables
  • Quantifiers
  • Methods of proof
  • Elementary set theory
  • Operations with sets including indexed families of sets
  • Principle of mathematical induction and its equivalent forms
  • Cartesian products
  • Relations, equivalence relations, and partitions of sets
  • Functions, surjections, and injections
  • Cardinality of sets
Coordinator
Dr. Anthony van Groningen


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