Course Content and Outcome Guide for MTH 105

Course Number:
MTH 105
Course Title:
Explorations in Mathematics
Credit Hours:
Lecture Hours:
Lecture/Lab Hours:
Lab Hours:
Special Fee:

Course Description

Students engage in the discovery and exploration of selected non-traditional topics in mathematics. Possible topics include mathematics of social choice, geometry, statistics, probability, and discrete mathematics. Technology will be used where appropriate. Students communicate results in oral and written form. Prerequisites: WR 115, RD 115 and MTH 95 or equivalent placement test scores. Audit available.

Addendum to Course Description

This class is a terminal course, thus it does not directly support other courses in mathematics and other disciplines. As such, students wishing to take MTH 112 must still take MTH 111. The course serves the purpose of exploring mathematical ideas/concepts that can support a variety of disciplines. The course should cover few topics, but cover them in depth.
This course should be rigorous in that it challenges student to contemplate, understand, and synthesize mathematical concepts. The students should be able to communicate their understanding in a variety of ways. Instructors are encouraged to use technology to enhance the learning experience.
Instructors may be conditionally allowed to select and use alternative course materials instead of the SAC-approved textbook. All such materials must receive advance approval from the standing MTH 105 alternate course materials subcommittee, respecting time for review in advance of book order deadlines. Advance approval shall again be required before using any new or substantially revised version of such course materials. Interested instructors should consult their Math Department Chair for further details.

Intended Outcomes for the course

Upon successful completion students should be able to:

• Use appropriate mathematics, including correct mathematical terminology, notation and symbolic processes, to solve everyday problems.
• Recognize which mathematical concepts are applicable to a scenario, apply appropriate mathematics and technology in its analysis, and then accurately interpret, validate, and communicate the results.
• Support conclusions using logical thought, reflection, explanation and justification.
• Recognize that mathematics is sensible, useful and/or worthwhile in a variety of applications in everyday life and other academic disciplines.

Course Activities and Design

All activities will follow the premise that formal definitions and procedures evolve from the investigation of practical problems. It is the goal of this class that the investigation of practical problems will drive a desire to learn the mathematics necessary to understand and explain the practical application.   In-class time is primarily activity/discussion emphasizing problem solving techniques. Activities will include group work.

Outcome Assessment Strategies

  1. At least one individual or group project culminating in a written report and/or an oral presentation. 
  2. In-class exam: proctored, closed book examination
  3. At least two of the following additional measures:
    1. Take-home examinations
    2. In-class exams
    3. Graded homework
    4. Quizzes
    5. In-class activities
    6. Portfolios
  4. Optional Additional Assessment Strategies
    1. Individual student conference
    2. Attendance

Course Content (Themes, Concepts, Issues and Skills)


Course content will include some of the following topics:

Select three to five topics

  1. Apportionment
  2. Fair Division
  3. Voting Theory
  4. Exponential Growth/Decay applied to populations and financial situations.
  5. Game Theory
  6. Queuing Theory
  7. Coding/ Code Checking (Error coding)/ Code Breaking/Cryptography
  8. Set Theory
  9. Statistics
  10. Probability
  11. Counting techniques €“ Combinations, Permutations
  12. Boolean Algebra
  13. Graph Theory
  14. Fractal Geometry
  15. Non-Euclidian Geometry
  16. Tilings
  17. Symmetry, Sequences, Shapes in Nature