MA 1830 - Transition to Advanced Topics in Mathematics

• 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

• None

• 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