University of Northern Colorado       SCHOOL OF MATHEMATICAL SCIENCES
Syllabus

Course: Math 120 - Mathematics and Liberal Arts               Credit: 3 units

Course Description: Prerequisite: at least one year of high school algebra with grade of "C" or better or intermediate algebra; ACT-Math score above 18 or equivalent. Topics include sets and logic; linear, quadratic, exponential and logarithmic models; interest theory, loans, annuities; probability and descriptive statistics. At least one additional topic is chosen from: Euclidean and non-Euclidean geometries; introduction to calculus; applied mathematics (e.g. voting and election theory; network theory).

Course Objectives: The primary objective of the course is to develop understanding of the techniques involved in the construction of mathematical models using problem solving strategies from mathematics and computer science. Given a situation to be modeled with mathematics, presented in the form of a real life problem or in the more structured format of a word problem, students will be able to evaluate the posited situation, propose a solution method for, and solve, the problem. Students should also have the ability, by the end of the course, to analyze solution(s) and discuss restrictions on their accuracy and applicability.

General Education Council Expectations met by Math 120:
  • The student will demonstrate proficiency in the use of mathematics and/or statistics to structure their understanding of and investigate questions in the world around them.
  • The student will demonstrate proficiency in treating mathematical and/or statistical content at an appropriate level.
  • The student will demonstrate competence in the use of numerical, graphical, and algebraic representations.
  • The student will demonstrate the ability to interpret data, analyze graphical information, and communicate solutions in written and oral form.
  • The student will demonstrate proficiency in the use of mathematics and/or statistics to formulate and solve problems.
  • The student will demonstrate proficiency in using technology such as handheld calculators an computers to support their use of mathematics and/or statistics.
Special Needs: Students who believe they may need accommodations in this class are encouraged to contact Disability Support Services, (970) 351-2289, as soon as possible to ensure that accommodations are implemented in a timely fashion.
Course Content: Major Study Units (All of topics 1-5 and at least one of 6-10 are covered):
1. Logic and Problem-Solving
  • Sets, Venn Diagram Models
  • Logic and Argument Analysis
  • Units of Measurement
  • Problem Model Strategy
2. Critical Thinking with Quantitative Information
  • Percentages
  • Relative Magnitude
  • Understanding Error
3. Functions and Modeling
  • Linear Models
  • Quadratic Models
  • Exponential Models
  • Logarithmic Models
4. Finance
  • Interest Theory
  • Annuities
  • Loans
  • Income Taxes
  • Federal Budget
5. Statistics and Probability
  • Statistical Study Design
  • Statistical Tables and Graphs
  • Correlation and Causation
  • Fundamentals of Probability
  • Central Limit Theorem
  • Risk Theory
 
6. Basic Calculus
  • Functions and Rates of Change
  • Infinitesimals and the Slope of a Curve
  • The derivative
  • Estimating Areas - Riemann sums
7. Geometry and Art
  • Euclidean and Non-Euclidean Models
  • Perspective
  • Modeling Nature with Fractals
8. Putting Statistics to Work
  • Variation
  • Distributions
  • Hypothesis Testing
9. Mathematics and Politics
  • Elections
  • Voting Theory
  • Apportionment
10. Mathematics and Business
  • Network Analysis
  • Hamiltonian Circuits
  • Scheduling
 

Instructional Strategies: There are three major instructional strategies in teaching the course: an emphasis on effective writing about mathematics, appropriate use of technology, and the rule of three.
Written assignments in the course:
- a project that includes an essay of at least 1100 words,
- homework assignments which include short essay answer explanatory questions in addition to some application and exploration problems,
- exam questions that require explanation and/or justification, in full sentences, of solutions.
Technology, in particular a graphing calculator along with its manual (or an equivalent computer program with manual), are used to help each student think about and analyze mathematics. In addition to the traditional use as a simple calculational tool, students are helped to master the graphing and basic programming capabilities of their calculators in order to better visualize models and estimate solutions.
The semiotic "rule of three" means that concept, symbols, and words are investigated for each topic. The most common interpretation of the rule of three in mathematics is to have students explore the geometric, numeric, and algebraic views for topics.

Methods of Evaluation: Assessment of student learning is accomplished via at least two in-class examinations, two projects (at least one of which is an individual research project whose outcome is either a written report or an oral report accompanied by a written abstract; the other project culminates in an essay of at least 1100 words involving a draft step - the preferred topic for this essay is the student's mathematical autobiography), and a comprehensive final exam. Lab sessions on a computer or using graphing calculators which illustrate the topics discussed in class are necessary and are to include assessment of technological mastery through either quizzes or short essay assignments.

Bibliography

  1. Bennett, J. O. and W. L. Briggs (2005). Using and understanding mathematics: A quantitative reasoning approach,3rd edition, Addison Wesley.
  2. J. O. Bennett, W. L. Briggs, and C. Mulcahy (2005). Student Solutions Guide for Using and understanding mathematics: A quantitative reasoning approach, Addison Wesley.
  3. Bleier, R. (Ed.) (1986). Feminist Approaches to Science, Pergamon Press.
  4. COMAP project (1994). For all practical purposes: introduction to contemporary mathematics, Freeman and Co., New York.
  5. Driver, R. D. (1995). Why Math? Springer-Verlag.
  6. Fadiman, C. (1958; reprint 1997). Fantasia Mathematica, Copernicus/Springer-Verlag.
  7. Giordano, F., W. P. Fox, and M. Weir (1997) An Introduction to Mathematical Modeling,Brooks/Cole.
  8. Gleick, J. (1987). Chaos, Penguin.
  9. Hoffman, P. (1988). Archimedes' Revenge, Fawcett.
  10. Hofstadter, D. R. (1979). Godel, Escher, Bach: An Eternal Golden Braid, Harper.
  11. Ifrah, Georges (2000). The Universal History of Numbers, Wiley & Sons.
  12. Mesterton-Gibbons, Michael (2001). An Introduction to Game-Theoretic Modeling,AMS.
  13. Staszkow, R. and R. Bradshaw (1995). The MathematicalPalette, 2nd ed., Saunders College Publishing.
  14. Staszkow, R. and R. Bradshaw (1995). Student Study Guide to Accompany the MathematicalPalette, 2nd ed., Saunders College Publishing.
  15. Taylor, A. D. (1995). Mathematics and Politics: Strategy, Voting, Power, and Proof, Springer-Verlag.
Prepared by S. Hauk, 22 August 2003; Rev. 8/24/04; Rev. 8/23/05.