Math 320 syllabus
Foundations of Mathematics (W)
Course Description: A transition to higher mathematics with an emphasis on proof techniques. Topics include symbolic logic, elementary set theory, induction, relations, functions, and the structure of the number system. Mathematics and Statistics majors are encouraged to take MA 320 as soon as possible after completing MA 125.
Suggested Text: Bridge to Higher Mathematics, by Sam Vandervelde.
Coverage: Chapters 1 through 7.
Learning outcomes: Upon the successful completion of the course a student will:
- Write mathematics and proofs in a clear, concise, logical, and correct way;
- Be able to state and verify the rules of formal logic and apply them to read and write mathematical arguments;
- Be able to state, justify and apply various proof techniques (direct, by contradiction, by contrapositive, and by induction)
- Be able to state, justify and apply the rules of elementary set theory and explain the role of set theory in mathematics;
- Be able to state the definition of a relation;
- Be able to state, verify and apply some properties of a relation (especially, order relations, equivalence relations, and the application of the latter to partitions of sets);
- Be able to state the definition of a function;
- Be able to state, verify and apply some properties of a function, particularly injectivity and surjectivity.