This course is especially intended for students who will major in areas which do not require further mathematics. The goal is to stimulate interest in mathematics in new ways, while perfecting basic logical and mathematical skills.
Suggested textbook: A Survey of Mathematics with Applications, Expanded 8th Edition by Angel, Abbott, and Runde.
Liberal Arts Math; Math Survey Course;
Two years of high school algebra
Upon successful completion of this course, the student should be able to:
1. Choose the winner of an election using the plurality, Borda count, plurality with elimination, and pairwise comparison methods.
2. Show that the plurality, Borda count, plurality with elimination, and pairwise comparison methods violate at least one of the fair and reasonable standards for a fair and sensible voting system.
3. Use principles of graph theory and networks to solve routing problems.
4. Discuss the development of various systems of numeration throughout history.
5. Perform arithmetic operations in other bases.
6. Comment on the historical contributions of other cultures to mathematics, including the development of irrational numbers and the Golden Ratio.
7. Classify real numbers into subsets by their inherent properties.
8. Discuss closure of a set under a given operation.
9. Generalize clock arithmetic to modular arithmetic.
10. Recognize arithmetic and geometric patterns in the world as they relate to linear and exponential growth, respectively.
11. Graph a system of linear inequalities to model a situation involving linear constraints.
12. Use linear programming concepts to determine the optimal solution.
13. Calculate simple and compound interest.
14. Calculate annual percentage rate.
15. Find the finance charge, average daily balance, and monthly payment on a loan.
16. Find the annual add-on interest rate being used for a loan.
17. Find the future value of an investment.
This site is a rich and growing source of materials pertaining to the history of mathematics including biographies of mathematicians, mathematics in various cultures, time lines, famous curves (with Java interactivity), overview of math history, in-depth coverage of a large number of history topics, and more. Individual pages contain many cross-links and material is well written and useful for both casual and experienced users. There is also a searchable quotation index as well as a selection of topics on the history of mathematics education and Indian mathematics. Faculty as well as students will find much here to enrich their mathematical understanding and enjoyment.
The Geometry Center, formerly housed at the University of Minnesota, is one of five main areas in the Science U web site (others include a library and an observatory). It contains a variety of appealing material, both textual and visual, including interactive exhibits, online simulations, graphics software and a library of reference materials pertaining to geometric tilings and polyhedra. The three main sub topics are "Triangle Tilings and Polyhedra", "Symmetry and Tiling" and "Tetrahedral Puzzles", with "Symmetry and Tiling" receiving the most emphasis.
The history of the abacus along with a virtual abacus that students may manipulate. Well-written. Most students know what an abacus is but have never used one; they find the virtual abacus to be quite interesting and can actually see place value in action.
While chaos theory is beyond the grasp of Liberal Arts Math students, they are afforded an engaging test of their analytical reasoning skills while playing the chaos game. Most enjoy the challenge--some challenge themselves with the advanced levels. Try to beat the computer by hitting specific targets via the moves of an iterated function system. This game allows students to understand the construction of the Sierpinski triangle via the chaos game.
This site has a wide-ranging collection of interesting puzzles, games, and recreational-type math activities. The emphasis of this site is on teaching and learning and the author makes every effort to engage the student/reader in the exploration and discovery process; the level of interactivity is outstanding. Thoughtful solutions are presented and the reader is guided to an analytical understanding of the underlying mathematical principles involved. In some instances alternative solutions are presented; in others, applications to other mathematical fields are described. Altogether, this section of Cut-the-Knot contains a wealth of educationally effective materials.
Cut The Knot! is a rich and wonderful collection of mathematical miscellany designed to entice the reader to experience mathematics at its delightful best. Alexander Bogomolny has developed an extensive collection of mathematical materials including many interactive java applets of his own creation. The main topical content areas are Games and Puzzles, Arithmetic/Algebra, Geometry, and Probability; these are accompanied by other sections on Interactive Activities, Proofs, Math as a Language, Eye Opener java applets, Analog Gadgets, Did You Know?, Things Impossible, and the CTK Exchange, a discussion forum for math students, faculty, and aficionados. In addition, there is an excellent collection of links to other math resources with accompanying annotations. This site is highly interactive and one can sense the author's fascination with mathematics and his desire to convey this to his readers. The main page also features over sixty articles from the author's monthly math column.
This excellent site contains a large and interesting selection of material on Fibonacci Numbers and their myriad related concepts. It includes web and text references to the rich literature of Fibonacci numbers. It also features a variety of images, graphics and animations. Many of the topics include student investigations for NCTM standard type explorations. The content includes standard motivational examples and applications in nature, but also mathematical explanations and puzzle pages. The site has already won several awards. The two initial pages on Fibonacci Numbers and Nature should be very effective at attracting and holding student attention with eye-catching and interesting natural examples. The first starts with the traditional rabbit problem, familiar to many students, and leads in to many variants involving other animals and plants. The material is written in a friendly easy-to-read style and includes many visuals, some of which are animated.
This site provides a comprehensive and easily accessible collection of material on prime numbers - research, records and resources, ranging in level from prime number trivia for a general audience to traditional proofs for an upper-division undergraduate and reference resources for a faculty member. It does not feature flashy images or animations but it has a lot of content written in a pleasant, readable style. The site includes useful utilities, options to interact with the author, and many resources. This site is potentially more effective than some larger, less focussed sites. It features a pleasant, conversational writing style and allows entry as a general user simply interested in learning about the concept of prime numbers, or as a more advanced user interested in the mathematical proofs behind the examples. It also caters to those specifically interested in joining a search for the next largest prime number.