Mathematics: Liberal Studies Requirements

Math 117 Fundamentals of Mathematics 1

Math 117 reviews the development of elementary math concepts from basic number sense to algebra. Emphasis is on mastery of the content as well as developing an understanding of basic arithmetic algorithms involving whole numbers and rational numbers. How children understand and perform math tasks is studied. This course is designed according to the State of California and the Biola School of Education standards.

Math 118 Fundamentals of Mathematics 2

Math 118 reviews the development of math concepts from algebra to probability and statistics to geometry. Emphasis is on mastery of the content as well as developing an understanding of how children learn and perform math tasks in the above content areas. This course is designed according to the State of California and the Biola School of Education standards.

Focused Area of Study Requirements

The requirements for the mathematics focused area of study consists of three lower division courses and one upper division course selected from the approved list:

Lower Division

  • Math 101 — Precalculus
  • Math 103 — Calculus for Management Sciences
  • Math 105 — Calculus 1
  • Math 106 — Calculus 2
  • Math 112 — Discrete Structures
  • Math 130 — Honors Nature of Math
  • Math 210 — Introduction to Probability & Statistics
  • Math 291 — Linear Algebra

Upper Division

  • Math 315 — Abstract Algebra I
  • Math 318 — Biostatistics
  • Math 331 — Probability
  • Math 332 — Statistics
  • Math 341 — Classical Geometry
  • Math 415 — Number Theory & History of Math

Rationale

The rationale for including three lower division courses in the requirement is that these courses present significant extensions of the problems and concepts required for elementary and middle school mathematics. At the upper division, many courses are so abstract as to provide little help for the prospective elementary teacher. Also, many upper division courses require at least 2 or 3 semesters of calculus (and sometimes additional courses) as prerequisites. Inclusion of such courses as a requirement would make it very unlikely for many students to pursue this focused area of study. On the other hand, a well-qualified student may choose to select two lower division courses and two upper division courses.

The list of approved courses provides alternatives for students from which to choose based on their background and interests. In order to serve as a guide for those choices and illustrate the common combinations, five options have been indicated below.

All options provide the student with exposure to statistics. Options 1-3 are the broadest, and would probably appeal to the largest percentage of students. Carefully selected courses allow students to pursue particular curricular areas in greater depth. Options 4 and 5 provide opportunities of this type, and may appeal particularly to students with an especially strong background in mathematics from high school. Option 4 requires the strongest prerequisite background, and provides the student with an especially strong concentration in probability and statistics. Option 5 has an advanced algebra focus.

Option 1 Option 2 Option 3 Option 4 Option 5
Math 101 Math 101 or 103 or 105 Math 101 or 103 or 105 Math 105 Math 112
Math 103 or 105 Math 112 Math 112 Math 106 Math 210
Math 112 or 130 Math 130 or 291 Math 210 Math 210 or 318 Math 291
Math 318 Math 318 Math 341 or 415 Math 331 Math 315

The following will outline how the courses proposed would provide a student with the background to develop core curriculum in mathematics for grades K-8, based on the Mathematics Framework for California Public Schools.

Math 101 builds on the base of Math 117 and Math 118 (required for all Liberal Studies students) to develop and illustrate the concept of function and to show how functions are used to model real-world situations in disciplines such as business, physics chemistry, and geology. Coordinate geometry is developed, and related to problem solving. Algebraic and geometric solutions to problems are compared.

Math 103 continues and extends the study of functions (including logarithmic and exponential functions) and coordinate geometry. Basic techniques of graphing and algebra are used extensively. Problem-solving and applications are stressed.

Math 105 continues and extends the study of functions and coordinate geometry described above under Math 101. Basic techniques of graphing and algebra are used extensively. Problem-solving and applications are stressed. Technology is utilized.

Math 106 continues and extends the study of functions (including stress on inverse functions) and coordinate geometry described above under Math 105. Basic techniques of graphing and algebra are used extensively. Problem-solving and applications are stressed.

Math 112 builds on the base of Math 117 to develop the fundamental concepts of sets, relations and functions, especially in a discrete setting [especially appropriate for the kindergarten through grade 8 learners]. Number base systems are discussed, as are combinatorial concepts and problem-solving. Basic concepts of probability are also introduced in the discrete context, building on Math 118.

Math 130 includes topics from number theory, Euclidean and non-Euclidean geometry, algebra, analytic geometry, probability, set theory and infinite sets. Math is viewed in its cultural and historical settings with connections to literature and philosophy.

Math 210 develops the basic concepts of probability and both descriptive and inferential statistics. A broad variety of applications are illustrated.

Math 291 develops the study of problems from algebra and coordinate geometry, such as system of linear equations, coordinate transformations, etc.

Math 315 develops some concepts foundational to various number systems, including finite systems. Some concepts also apply to geometrical problems.

Math 318 develops the basic concepts of probability and both descriptive and inferential statistics. A variety of applications are presented from the biological and health sciences.

Math 331 includes a treatment of basic set theory and combinatorics for use in discrete probability. Continuous random variables are also studied. This treatment is much more in-dept that in Math 118 and Math 112. Problem-solving and conceptual understanding are both stressed as a mature level.

Math 332 continues Math 331, and provides a study of the theory of mathematical statistics. The student who completes Math 331 and 332 would have excellent background to develop the expanding probability and statistics portion of the elementary and middle school curriculum.

Math 341 develops elementary and advance tops of Euclidean geometry well beyond Math 118. Compass and straightedge constructions in plane geometry are studied, giving geometry a hands-on approach. Problem-solving and conceptual understanding are both stressed.

Math 415 develops classical number theory on the foundation of such principles as the Fundamental Theorem and Arithmetic and the Division Algorithm. The properties of greatest common divisor and lease common multiple are studied, as are divisibility issues. Prime numbers are studied extensively. A significant focus of this course is on the development and examination of conjectures by students. The role of induction and deduction is discussed. This course also includes a study of the history of mathematics. In this context, the value of mathematics as it has been perceived in different cultures is considered. Students are required to write a research paper, and make oral presentations.

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