Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 108: Intro to Abstract Math
Approved: 2003-03-01 (revised 2013-01-01, J. DeLoera)

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
A Transition to Advanced Mathematics, 7th Edition by Douglas Smith, Maurice Eggen, and Richard St. Andre; Brooks-Cole Publishing; $136.00-193.00 via Amazon Books.
Search by ISBN on Amazon: 978-0495562023

Prerequisites:

Completion of course MAT 21B (or equivalent).

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

1-5

1.1 – 1.6

Logic and proofs. Lighter on the initial material; Emphasis on proof techniques.

6-10

2.1 – 2.5

Sets and induction. Emphasis on mathematical induction and equivalent principles.

11-13

3.1 – 3.3

Equivalence relations and partitions.

14-17

4.1 – 4.4

Functions. Emphasis on onto and 1-1 functions.

18-21

5.1 – 5.3

Cardinality, Do in full detail up to Theorem 5.3.8, which requires the Axiom of Choice.

22

5.4 and 5.5

Order of cardinals, comparability. Emphasis on section 5.4, but omit proof of Cantor-Schroeder-Bernstein Theorem and do 5.5 lightly.

23-26

6.1 – 6.4

Groups, subgroups, and operation preserving maps.

27

6.5

Rings and fields.

28


Connection to vector spaces.

Additional Notes:

This is a total of 28 lectures, which leaves two lectures for exams, introduction, etc., in quarters in which there are 30 lectures. This syllabus is constructed with the use of the Tuesday or Thursday class as a discussion section. If Tuesdays or Thursdays are used for a lecture, the number of lectures on the topics above must be expanded proportionately.

Learning Goals:

The primary goal of 108 is to teach students the fundamentals of mathematical thinking and clear writing of mathematical arguments. This is the a beginners exposure to the notion of proof, to the language used by mathematicians (e.g., implications, quantifiers, notion of contradiction, induction). Most of the explanations and practice will use examples from basic set theory, basic combinatorics, and algebra.

Mastery of this course enhances the ability to write clear well-organized scientific arguments. Mastery of this course also supports the development of clear analytical thinking.

Assessment:

To assess the learning outcome for this course, the course will be graded through regular homework (involving considerable writing) midterm examinations, and a comprehensive final exam. This course satisfies GE writing requirement and students are required to work on writing projects, which receive comment from the instructor.