MATHEMATICS 301

Foundations of Mathematics

John Travis
MCC 206
925-3817 (voice mail)
travis@mc.edu (email)

Class Photos | Textbook | Course Description | Course Meetings | Grading

TEXTBOOK: A Transition to Advanced Mathematics, 8th edition, by Smith, Eggen and St. Andre; Brookes/Cole Publishing Company.

COURSE OUTLINE :  Mathematics as a course of study falls somewhere between a science and an art.  However, special characteristics distinguish mathematics from the humanities and from other sciences.  Particularly important is the kind of reasoning that typifies mathematics. The natural or social scientist generally makes observations of particular cases or phenomena and seeks a general theory that describes or explains the observations. This approach is called inductive reasoning and is tested by making further observations.  If the results are incompatible with theoretical expectations, the scientist usually must reject or modify the theory.

A mathematician frequently uses inductive reasoning to describe patterns and relationships among quantities and structures. The characteristic thinking of the mathematician, however, is deductive reasoning, in which one uses logic to draw conclusions based upon statements accepted as true.

A goal of this course is to give the student a working knowledge of the basics of mathematical logic and the how to construct formal mathematical proofs, both of which are fundamental to deductive reasoning. Topics include set theory, logic, axiom systems, proof techniques, relations, functions, and cardinality. Emphasis will be given to applying proof techniques to material in Number Theory.

Further, this course will introduce students to the mathematical literature and provide opportunity to experience current mathematical research. Students will prepare summary reports for periodical articles chosen according to their interests and present at least one of these summaries to the class.

Foundations of Mathematics is a required course for all students pursuing an undergraduate degree in Mathematics at Mississippi College and is a prerequisite for most upper-level courses. This course is also required for students pursuing the 18-hour Minor in Mathematics. It is also appropriate for scientifically inclined students seeking a mathematics course which focuses more on logic and mathematical proofs.

RATIONALE: As students advance to upper level mathematics courses, they constantly need to apply various proofing techniques. This course is designed to prepare them for these techniques, as well as other topics needed in the advanced courses. This course is required of the mathematics majors and minors and serves as an elective for others.

COURSE CONTENT: Set theory, logic, axiom systems, proof techniques, relations, functions, and cardinality, proof techniques.

INSTRUCTIONAL PROCEDURES/TECHNIQUES: Various instructional procedures are used including: lecture, exams, questions and answers, class discussions and presentations, written work, online work.

PREREQUISITES: Mat 122

MEETINGS: This class meets as scheduled. You are expected to be in class on time. A student cannot miss more than 25% of the class meetings and receive credit for the course. Further, attendance will be necessary in order to understand the material and make a good grade. The student is responsible for work and material missed when absent. Cheating in any way will be properly rewarded according to University policy.

INTERMEDIATE-POST ASSESSMENT: There will be at least two exams during the semester. Further, students will be expected to present their written homework on the board in class with a record kept to measure quality. Also, online homework problems, a Book Review, and several Periodical Review written assignments will be graded. The average of these non-test grades will be averaged together. Your final average will be computed by using a non-weighted average of the two exam grades with the daily average.

Periodical Review: This course includes an information literacy emphasis as part of U Research, Mississippi College’s Quality Enhancement Plan (QEP). In particular, students in this course will focus on the U Research Student Learning Outcomes:

SLO 2b: The student will develop skills for retrieving information using a variety of methods and systematically manage the information and its sources

SLO 3b: The student will evaluate information and its sources using appropriate criteria and identify main ideas and their potential relevance, summarizing and synthesizing key ideas

SLO 4b: The activity will assess how well the student communicates the product to the reader.

Students who have transfer credit for ENG 102 will need to satisfactorily complete a short information literacy tutorial as an introduction to research concepts and resources available at Mississippi College. This must be completed before the mid-term exam.

For the non-exam grade: