Approval Status
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
Course Type
Lower Division