Approved

## Date Reviewed

March 2014
A survey course in mathematical concepts and mathematics in culture. Topics to include mathematical reasoning and four additional topics selected from number theory, probability, statistics, mathematical modeling, contemporary applications, geometry, and the history of mathematics. Recommended for liberal arts students. Student Learning Outcomes: Upon completion of the course, students will be able to: 1. Apply the principles of inductive and deductive reasoning. 2. Demonstrate proficiency in mathematical skills and conceptual understanding within four of the following topics: number theory, probability, statistics, mathematical modeling, contemporary applications, geometry, and the history of mathematics. 3. Apply mathematical concepts to a variety of real-world problems. Objectives: Upon completion of the course, students will be able to: 1. Define inductive reasoning, and apply to patterns and sequences. 2. Define deductive reasoning, and apply to logic and sets. 3. Demonstrate ability to perform four of the following objectives: A. Define various sets of numbers and use number systems of different bases. B. Apply counting techniques, permutations, combinations, and probability models. C. Define frequency distributions and measures of central tendency and dispersion, and create graphical displays of data. D. Apply mathematical models such as linear, quadratic, exponential, and logarithmic, to real-world problems. E. Understand topics within contemporary mathematics, such as voting and apportionment, financial mathematics, graph theory, linear programming, and applications of matrices. F. Define and apply concepts of areas, volumes, Euclidean and non-Euclidean geometry, and selected other topics in geometry. G. Describe the historical development of mathematics, the role of theorem and proof in mathematical thought, and significant mathematical results and mathematicians. Topics and Scope Instructors will include mathematical reasoning (I) and four additional topics chosen from II through VIII. I. Mathematical reasoning A. Inductive reasoning 1. Patterns 2. Sequences B. Deductive reasoning 1. Logic 2. Sets II. Number theory A. Sets of numbers (e.g. prime, perfect, amicable, etc.) B. Numeration systems and number bases C. Additional topics may be chosen from identification numbers, encoding data, modular arithmetic, and cardinal numbers III. Probability A. Counting techniques B. Rules of probability C. Conditional probability D. Probability models and simulations IV. Statistics A. Frequency distributions B. Measures of central tendency and dispersion C. Graphical display of data D. Additional topics may be chosen from normal curve, estimation, and margin of error V. Mathematical modeling A. Linear, quadratic, exponential, and logarithmic models B. Regression models VI. Contemporary applications Types of applications to be chosen by instructor, but could include one or more of the following: A. Linear programming B. Matrices C. Financial mathematics D. Voting and apportionment E. Graph theory VII. Geometry A. Areas and volumes B. Euclidean geometry and deductive systems C. Non-Euclidean geometry D. Additional topics may be chosen from conic sections, trigonometry, fractal geometry, polyhedra, symmetry and tessellation VIII. History and culture of mathematics A. Overview of the historical development of mathematics B. Role of theorem and proof in mathematical thought C. Significant mathematical results and mathematicians

Lower Division