# Student Handbook: Learning Outcomes

All students will be appraised of the departmental learning outcomes objectives which are as follows:

Upon the completion of the core curriculum in Mathematics, the student should be able to:

1) Analyze polynomial and transcendental functions of one or more variables with respect to:

a) operations of functions, graphs, existence of inverse functions
b) existence of limits
c) continuity, differentiability (both explicit and implicit) and partial differentiation.
d) integrability with techniques of integration
e) representation of functions through infinite series
f) interpretation and summary of information from graphs of functions
g) be able to prove limit theorems in simple cases by using Epsilon - Delta methods

2) Demonstrate an understanding for the applications of the derivative and the integral in:

a) maxima and minima points, increasing and decreasing functions, concavity,and the Mean Value Theorem
b) relative rates, velocity and acceleration
c) applying the Fundamental Theorem of the Calculus
d) calculating area, volumes, and arc length

3) Understand the fundamentals of vector space calculus with:

a) representations and operations
b) vector functions
c) directional derivatives, gradient, tangent planes
d) line and surface integrals with Green's and Stoke's theorems

4) Understand the theory of linear algebra in:

a) linear systems and the solution of such systems
b) special types and properties of matrices
c) elementary matrices and their importance in proofs
d) transformations
e) vector spaces, determinants, and eigenvalues
f) abstract inner product spaces

5) Organize and synthesize mathematical information into logical proofs:

a) principles of logic
b) methods of proof: proof by induction, contradiction, contraposition
c) understand the axiomatic development of consistent mathematical systems and the importance of counter examples
d) interpret mathematical statements distinguishing hypotheses and conclusions
e) distinguish between conjecture and rigorous mathematical proof

Upon the completion of the Mathematics Program, the student should be able to:

6) Demonstrate quantitative literacy:

a) be able to analyze, interpret, and present data in a logical and scientific manner.
b) know basic counting methods, and basic knowledge of statistics and probability

7) Demonstrate an understanding of the principles and techniques of applying mathematics to real world problems:

a) use techniques of linear algebra and differential equations to solve various applied problems
b) understand the importance and widespread existence of nonlinear problems and the role of the linear theory in developing insight into these problems
c) grasp the concept of "dynamical" systems and their importance in comparison to "static" problems

8) Understand the role of the computer in mathematics by implementing and understanding the importance and limitations of algorithms for:

a) numerical methods for approximating integrals, series and numbers
b) different methods for graphing continuous and discontinuous functions in two and three dimensions
c) numerical methods for approximating solutions of linear systems and differential equations

9) Communicate clearly and effectively in an organized fashion the basic concepts and principles of mathematics, from calculus to modern applications and theory:

a) communicate, in both oral and written fashion, mathematical concepts and methods in a precise manner
b) present historical perspectives and implications of mathematical ideas
c) understand research in mathematics by actively doing research in a specific area
d) analyze some application problems using modeling techniques to observe patterns, interconnections, and underlying structures