MATHEMATICS PROGRAM LEARNING OUTCOMES
The mathematics program at Chaminade University provides
requirement in mathematics (MA100 and MA103) to all undergraduate students, teaches
supporting mathematics courses to other sciences disciplines (Biology, Forensic Science,
Computer Science, Chemistry, and Physics), and offers higher level mathematics courses
to students who are pursuing a minor in mathematics.
The Mathematics program’s objectives are to enable students:
1. to demonstrate the understanding and skills in reading,
communicating mathematical contents which are integrated into other disciplines or
appear in everyday life;
2. to gain understandings of and skills with logical thinking, deductive and inductive
3. to articulate the understanding of more advanced mathematical concepts and
quantitative skills to support the study of other disciplines, including skills with
numeric and symbolic computations, and problem solving using numeric, analytic
and graphic methods; and
4. to develop mathematical maturity to undertake higher level studies in mathematics
and related fields.
The program goals of the mathematics program will be
realized from the learning
outcomes of the main courses it is offering, as shown in Table 1 below.
Table 1. Learning Outcomes for Mathematics Courses
|Math course||Supporting which
course or degree
|MA 100||Fulfills Track-A
|1. Demonstrate the basics of logical thinking and
problem solving process.
2. Take a survey on the nature of calculation, numbers, and geometry.
3. Use basic knowledge in financial management, probability, and statistics to solve applied
problems in everyday life.
|MA 110, CH 102,
CH 203, AC 201,
BU 224, BU 324,
|1. Demonstrate skills to simplify polynomials
(including factoring), rational expressions,
radicals and rational exponents.
2. Produce solutions to various algebraic equations, linear and quadratic inequalities, and
systems of equations
3. Demonstrate the use of elementary graphing techniques.
4. Describe exponential and logarithmic functions, natural number functions and
|CH 203, CH 204,
PHY 151, MA 210
CS/CIS, and CH minor
|1. Describe basic concepts of functions and their
graphs (including increasing and
decreasing functions, transformation of functions, composite functions, extreme values
of functions, and inverse functions).
2. Understand polynomials (including theorems on the zeros of polynomials), rational
functions, exponential and logarithmic and trigonometric functions and demonstrate
more graphing techniques, sketching their graphs
3. Understand definitions of trigonometric functions, and apply the principles of
trigonometry to the solution of equations and verification of identities.
|PHY 251, MA 211
requirement for FS,
BIO, and PHY minor
|1. Find limits of functions and discuss
continuity of functions.
2. Find derivatives of algebraic and trigonometric functions (including implicit
differentiation, higher order derivatives), and use derivatives to solve applied problems
(including related rates, local extrema, Rolle’s theorem and the Mean Value theorem, the
first and the second derivative tests, concavity, and asymptotes).
3. Understand the Fundamental Theorem of Calculus.
4. Find integrals of some algebraic and trigonometric functions, use the techniques of
integration by substitution and numerical integration, and use integrals to solve applied
problems (simple area problems).
|PHY 252, PHY 253
for FS, BIO (BS
degree), and PHY
|1. Compute derivatives and integrals for common
transcendental functions, and analyze
2. Find indefinite and improper integrals using different integration techniques (including
basic integration rules, integration by parts, trigonometric substitution, partial fractions),
apply L'Hospital’s rule for indeterminate forms.
3. Determine the convergence or divergence of infinite series by applying various
techniques (including the integral test, P-series, comparison test, alternating series, the
ratio and roots tests). Perform standard operations with convergent power series, and
find Taylor and Maclaurin representations.
4. Write parametric equations of conic sections; sketch their graphs in polar and Cartesian
coordinates. Graph polar equations.
|PHY 310, PHY 311||1. Define and use vector operations (including
dot product and cross product) in two and
three dimensions, find parametric equations of a line, standard equation of a plane in
space, and understand cylindrical and spherical coordinates.
2. Differentiate and integrate vector-valued functions and find velocity and acceleration
along a space curve, curvature and arc length. Determine position function for a
3. Define and use the standard techniques of multivariable calculus, both differential and
integral, and utilize them to solve selected applied problems (by applying partial
derivatives, directional derivatives, gradients, the chain rule, differentials, the method of
Lagrange multipliers, double and triple integrals, center of mass and moments of inertia,
or change of variables).
4. Define vector fields; find the line and surface integrals, find work, circulation and flux;
determine conservative fields and path independence, Green’s theorem, divergence
theorem, and Stoke's theorem.
|Major requirement for
CS and CIS
|1. Understand logic and propositional calculus,
and write a correct formal proof.
2. Understand relations and determine types of relations; reflexive, symmetric,
antisymmetric, or transitive.
3. Understand basics on modular arithmetic.
4. Understand fundamentals of graph theory, subgraphs, connection, trees, coloring,
Euclidian graphs (including the bridges of Konigsberg , traversable multigraphs).
5. Boolean algebra (optional).
|Major requirement for
|1. Understand Central Limit Theorem and its
application to confidence intervals of mean
and proportion; conduct hypothesis testing for mean, deviation, and proportion.
2. Understand correlation and regression; know how to perform linear regression analysis.
3. Test hypotheses involving one or two variances by using Chi-square and F distributions;
perform one-way and two-way analysis of variance.
Major requirement for
|1. Understand the definition of matrix (including
some types of matrices), matrix
multiplication, and algebraic properties of matrix operations; Perform elementary matrix
2. Solve systems of linear equations using matrices.
3. Understand vector spaces and subspaces, span and linear independence, basis and
dimension; identify and construct examples of elementary vector space ideas in
Euclidean n-space as well as in general vector spaces.
4. Understand the properties of determinants and find eigenvalues and eigenvectors and use
them in diagonalization problems and other applications.