PCC/ CCOG / MTH

Course Content and Outcome Guide for MTH 105

Date:
23-AUG-2011
Posted by:
Scot Leavitt
Course Number:
MTH 105
Course Title:
Explorations in Mathematics
Credit Hours:
4
Lecture hours:
40
Lecture/Lab hours:
0
Lab hours:
0
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 Math 112 or Stat 243 must still take Math 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.

 

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:

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