Indiana University of Pennsylvania Mathematics Department Indiana, PA 15705 Course Number: MA 117 Course Title: Principles of Mathematics Credits: 3 semester hours Prerequisites: none Catalog Description:This course is an introduction to the nature of mathematics, designed specifically as a first course for mathematics education majors to experience several facets of mathematics including deduction, induction, problem solving, discrete mathematics, and th eory of equations. Enrollment open to secondary mathematics education majors only.
Course Objectives: 1. To give the prospective secondary school mathematics teacher, at the beginning of his/her endeavors, an overview of the many threads that weave through the fabric of mathematics, e.g. logic, functions, sets, graphs, number, counting, and problem solvi ng. 2. To reveal the many facets of mathematics, including the inductive and deductive natures, the abstract and practical natures, and the beautifully simple and sometimes complex natures of the subject. 3. To provide an awareness of some of the more classical results in mathematics as well as current directions in mathematics. Course Outline and Schedule: I. Logic (7 hours) A. Propositions B. Compound propositions C. Tautologies and contradictions D. Negations of compound statements E. Arguments and validity, reductio ad absurdum F. Formal proof, conditional conclusion, and indirect proof G. Quantifiers, logical equivalence, negations H. Disproof by counterexample II. The Real Numbers (8 hours) A. Field properties B. Subsets of the real numbers and their properties C. Unique factorization of the integers D. Mathematical induction E. The order properties F. Some theorems related to the field of real numbers G. The real numbers as a complete ordered field III. Equations and Inequalities (5 hours) A. Linear and quadratic equations and inequalities B. Fundamental theorem of algebra C. Synthetic division D. Factor theorem, remainder theorem E. Rational root theorem IV. Functions (8 hours) A. Definitions B. Functional notation C. Domain and range of a function D. Special functions 1. absolute value 2. greatest integer 3. principle square root 4. exponential 5. logarithmic 6. trigonometric E. Algebra of functions F. Inverse functions and their graphs V. Complex Numbers (5 hours) A. As an extension of the real numbers B. Properties C. Trigonometric representation D. Powers and roots, DeMoivre's Theorem VI. Analytic Geometry (7 hours) A. Distance and midpoint formulas B. Slope and stright line equations C. The circle D. Other conic sections E. Polar coordinates, polar equations F. Parametric equations VII. Sets A. Theorems about sets, some proofs B. Cardinality and number C. Cardinality and infinite sets VIII. Combinatorics A. Counting procedures B. Permutations C. Combinations D. Binomial thoerem IX. Probability A. Probability experiments B. Classical and empirical probability C. Probabilities of compound events D. Conditional probability E. Binomial probability distribution F. Testing hypothesis X. Linear Programming A. Open inequalities in two variables - graphic solution B. Linear programming - graphic method C. Simplex method for problems with two variables D. Simplex method for problems with three or more variables E. The minimum problem and dualityIt is recommended that topics I. through VII. be completed. Topics VIII. through X. and other possible topics might be considered by the professor assigned to the course if an analysis of students' backgrounds warrant. The instructor is free to introduc e his/her own materials to supplement the course and to aid in meeting course objectives as given in the catalog description.
Text: Handouts provided by the instructor Evaluation: Examinations, quizzes, classroom participation
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