Marywood University Department of Mathematics Course Information for Math 120 Functions of Mathematics in the Liberal Arts Dr. Craig M. Johnson

This course demonstrates the importance and place of mathematics within the liberal arts. It is designed to implement NCTM (National Council of Teachers of Mathematics) curriculum standards. The topics are chosen specifically to:

• Strengthen estimation and computational skills
• Utilize algebra concepts
• Emphasize problem-solving and reasoning
• Emphasize pattern and relationship recognition
• Highlight importance of units in measurement
• Highlight importance of the notion of a mathematical function
• Display mathematical connections to other disciplines.

A typical semester course covers at most four of the following nine units each of which is a chapter of a textbook I have written entitled, "Functions of Mathematics for the Liberal Arts" to be published and available by Fall, 2008. Select any chapter listed below for ancillary material, sample test problems, FAQ, and useful websites. (Still under construction.)

The course grade is determined by 2 tests, 3 quizes, homework, 3 computer/calculator labs, and the final examination. The option also exists to research and write a paper on some mathematical topic of interest to the student. Over the years, a number of these papers have been very creative and interesting. A partial list of topics is displayed at the bottom of this page. Grading is based on mathematical correctness, organization of ideas, proper grammer, and quality of presentation. If you choose to report on a person, then you must effectively summarize that person's mathematical contributions and present some actual mathematics. Footnotes and a bibliography of at least three sources is required. Quotes must be referenced. These requirements dictate that any reasonably good paper must be at least four pages in length.

1. The Concept of Function Functions Around Us Creation of Functional Expressions The Graph of a Function Interpretation of Graphs	2. Astronomy and the Methods of Science Ancient Milestones The Two Great Systems Defense of Copernicanism And All was Light	3. Logic and Computer Science Statements and Connectives Truth and Consequences Tautologies and Syllogisms Computer Programming Structures
4. Functions of Personal Finance Interest and Effective Yield Annuities Amortization of Loans	5. Graph Theory Paths and Networks Euler Circuits Hamilton Circuits	6. Voting Methods Plurality and the Borda Count The Hare System Approval Voting
7. Number Theory in Music and Cryptology Residue Classes and Notes Transformations The Circle of Fifths Modular Arithmetic and Cryptology	8. Probability Sample Spaces and Events Introduction to Sets Probability and Properties	9. Statistics Representation of Data Dispersion The Normal Distribution Confidence Intervals

Past Topics of Student Papers

• Mathematics and Shakespeare
• Galileo and the Law of the Pendulum
• Leonardo Da Vinci and His Use of Mathematical Perspective
• Statistics of the Marywood Men's Soccer Team
• Statistics of Enrollment in Public Schools
• Math in Photography
• Logical Anlaysis of Alice in Wonderland
• Tautologies in Language
• The Contributions of Carl Friedrich Gauss
• Hypatia of Alexandria
• An Introduction to Kepler's Laws
• The Use of Mathematics in Stage and Theater Lighting
• Origins of Counting Systems
• The Creation of Boolean Algebra
• Adapting Mathematics for the Learning Disabled
• Mathematical Perspective in Art
• Biomass Energy
• When Zero Originated and How It Applies to Education
• Analysis of A Brief History of Time by Steven Hawking
• The Myth of How the Egyptians Constructed the Pyramids
• The Life and Contributions of Bertrand Russell
• Schoenberg: Atonality and the Twelve Tone System
• The Philosophy of Rene Descartes
• The Work of Galileo Galilei
• Kurt Godel : Systems of Logic
• Math Anxiety
• Copernicus and his Contributions
• The Works of Pierre De Fermat
• John von Neumann and the Computer
• Using Literature to Strengthen Math Concepts for Children
• The Importance of Fractals in our Lives
• Emmy Amalie Noether
• Mathematics in Basic Musical Theory
• Women in Mathematics: Through the Centuries

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Comments to Dr. Craig M. Johnson, Chair, Dept. of Mathematics: johnsonc@ac.marywood.edu

Last update: March 7, 2007

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