BA in Natural Science and Mathematics, Concentration in Mathematics, September 2011
Learning Outcomes: BA Mathematics
1:
Abi
lity
to U
se fo
rmal
Rea
soni
ng to
Pr
esen
t an
Arg
umen
t
2:
Dem
onst
rate
Con
cept
of “
Func
tion”
by
seve
ral m
eans
3: W
ritte
n an
d V
erba
l Com
mun
icat
ion.
A
ppro
pria
te U
se o
f Not
atio
n an
d V
ocab
ular
y. F
orm
ulat
ion
of C
onvi
ncin
g A
rgum
ents
in P
roof
s.
4: H
isto
rical
Kno
wle
dge
of M
athe
mat
ics
in o
ther
Cul
ture
s
5: A
pply
Mat
hem
atic
s Con
cept
s and
R
easo
ning
in re
late
d D
isci
plin
es.
(In
Futu
re P
lans
)
Required: M215 Calculus I, One Variable (LO 2) Calculate & Interpret Finite & Infinite Limits, Derivatives, Integrals Apply concepts of Derivatives and Integrals to Solve Applications Analyze physical phenomenon using derivatives and integrals M216 Calculus II, Sequences (LO 2) Calculate & Interpret Derivatives and Integrals including Improper Integrals of Functions
Determine the Convergence of Sequences and Series Illustrate a given Function as Expansion of an Infinite Series Math-M311 Calculus III, Several Variables (LO 2) Demonstrate an understanding of Vector Calculus Apply Partial Derivatives to Optimization Understand Multivariant Integration & its Applications
Math-M380 History of Math (LO 4) Understand the development of mathematics in various cultures Understand the history of various fields in mathematics Understand the Historical Effects of mathematics in other areas of science Understand the Historical Effects of mathematics in Liberal Arts Math-M393 Bridge to Abstract Mathematics LO 1 and LO 3 Demonstrate Basic Mathematical Logic: Propositions, Connectives, Quantifiers, Proof Techniques
Demonstrate Appropriate Use of Sets/Set Notation Define/Identify Relations: Cartesian Products, Equivalence Relations, Ordering Relations
Define/Identify Functions (Properties) Demonstrate Use of Cardinality with Respect to Sets Capstone (LO 1,2,3) Demonstrate an understanding of basic proof methods (e.g. induction, conditionals)
Demonstrate an understanding of properties of continuous functions (e.g. Extreme Value Theorem)
Demonstrate the ability to converse about the basic ideas in one advanced field of mathematics (e.g. discuss the definition of closure in the context of point set Topology)
Must Take 6 credit hours in Following 3 Courses: Math-M303 Linear Algebra LO 5 (in Future) Demonstrate understanding of Real and Complex Vector Spaces and Linear Transformations
Perform Operations on Matrices Solve System of Equations using Matrix Algebra
Math-M313 Differential Equations Demonstrate ability to use basic techniques to solve differential equations, analytically and numerically
Demonstrate ability to apply differential equations to problems involving models from biological and physical sciences
Math-M371 Numerical Methods Calculate & Interpret Roots, Derivatives, Integrals of function using Numerical Methods
Compare & Contrast Convergence Rates of Numerical Methods Determine Function that Fits a given set of Data points 30 Credit Hours from Following Courses: Math-M295 Readings/Research Variable Based Upon Topic Math-M312 Calculus IV Demonstrate understanding of Green’s Theorem & its Applications Demonstrate understanding of Stoke’s Theorem & its Applications Demonstrate understanding of Divergence Theorem & its Applications Math-M366 Statistical Inference Demonstrate understanding of basic Descriptive Statistics Demonstrate how to Construct Confidence Intervals Demonstrate how to Perform various Tests of Hypothesis Demonstrate understanding of Non-Parametric Statistics Demonstrate understanding of Analysis of Variance Apply Software Programs such as Stat Crunch in Analyzing Data M403 Modern Algebra I Demonstrate knowledge of Definitions of basic Algebraic Structures (Group, Ring, Integral Domain, Field)
Demonstrate ability to Prove basic Theorems in Abstract Algebra (e.g. prove: If H≤G is a normal subgroup, then G/H is a group)
Apply basic Principles of Ring Theory to prove Fermat’s Little Theorem and Euler’s Theorem
M405 Number Theory Demonstrate ability to apply Number Theory to Cryptography Demonstrate ability to apply theorems of Number Theory to questions of Divisibility and remainders
Demonstrate ability to Solve Diophantine Equations Demonstrate knowledge of History of Number Theory M406 Topics Variable Based upon Topic M413 Introduction to Analysis I Demonstrate Use of Induction as is Relates to Natural numbers Demonstrate Appropriate Use of Axioms of Real Numbers Define and Use Compactness, Completeness, Infimum, Supremum with Sets of Real Numbers
Demonstrate Knowledge of Sequences, Limits, Bolzano-Weierstrass Theorem, Subsequences
Apply Properties of Continuous and Uniformly Continuous Functions Math-M415 Elementary Complex Variables Demonstrate understanding of Representation of (sets of ) Complex Numbers in the Amagard Plane
Demonstrate the use of Differentiability Criteria to determine whether a function is Holomorphic (analytic)
Apply the Residue Theorem to evaluate Indefinite Integrals on the Real Line Apply Liouville’s Theorem to entire functions M421 Introduction to Topology
Define/Identify Basic Concepts of Topology Demonstrate Use of Subspaces and Continuity Homeomorphisms and Standard Topology of Rn Apply basic theorems about Finite Products of Topological Spaces to prove simple statements
Ability to Prove basic Consequences of Connectedness Ability to Prove basic Consequences of Compactness Ability to Prove basic Consequences of Separation Axioms Math-M447 Mathematical Models I Demonstrate ability to solve Linear and Non-Linear Programming Problems Demonstrate understanding of Principles of Operations Research Demonstrate ability to Solve Problems in Game Theory Demonstrate ability to Solve Distribution and Transportation Problems