MAT 118 Mathematical Thinking Fall 1999

Train of gears with multiplying power of 1012 (Leonardo da Vinci).

Fall 1999 Staff, Schedule and Homework

Review for Midterm I

Review for Midterm II

Review for Final

Prerequisite: score of 2+ or better on Mathematics Placement Examination.

The course will help students develop

• Appreciation for the intellectual scope of mathematics, and its connections with other disciplines.
• Quantitative thinking and problem solving abilities.

The course will give students a taste of several topics in mathematics, chosen according to two criteria: approachability by non-technically-oriented students, and relevance to their future activities or thought-processes. In each of these topics students will engage in the actual process of mathematical problem solving. So this course is not a general survey of the history of mathematics, nor a ``math for poets'' course. It will be a regular math course, with problem sets and problem-based examimations.

The text will be Mathematics, A Practical Odyssey by Johnson and Mowry (Brooks Cole).
Each student should have a scientific calculator.

• Weeks 1-3. Logical Reasoning and Problem Solving: Logical assertions, connectives, syllogisms, contradictions. Strategies for simple problem solving.
• Weeks 4-6. Numbers, Functions and Modeling: Arithmetic and algebra -- brief survey with exercises. Elementary functions: linear, powers, exponentials. Particular emphasis on the modeling of relationships between real-life quantities, visualization using graphs and the significance of graph features to the subject being modeled.
• Weeks 7-9. Combinatorics and Probability: Counting methods, permutations and combinations. Basic examples like Fibonacci sequence, Pascal's triangle. Elementary probability examples.
• Weeks 10-12. Growth and Change: Difference equations. The basic ideas of calculus.
• Weeks 13-15. Other topics as time permits, and according to instructor preference.