UTPB MATHEMATICS REORGANIZATION PLAN
Brian Hagler
February 12, 2016
Course Offerings
Freshman Service, 13xx (18 cr. hrs.):
Senior 43xx (3 cr. hrs.):
Certification Math. 1 (F3S3 )
Algebra 1 (S)
3 3
Certification Math. 2 (F S )
Real Analysis 1 (F)
Freshman, 14xx (12 cr. hrs.)
Precalculus (FS, 4 cr.)
Calculus 1 (FS, 4 cr.)
Calculus 2 (FS, 4 cr.)
Sophomore, 2xxx (6 F & 10 S cr. hrs.):
Intro to Statistics (F)
Calculus 3 (S, 4 cr.)
Intro to Differential Equations (S)
Mathematical Reasoning (FS)
Junior, 33xx (6 cr. hrs.):
Intro to Linear Algebra (F)
Intro to Vector Analysis (F)
Intro to Number Theory (S)
Intro to Probability (S)
Senior/Grad., 43xx/53xx (9 cr. hrs.):
Algebra 2 (F)
Real Analysis 2 (S)
Complex Variables
Linear Algebra
Numerical Methods
Topology
Probability
Differential Equations
Partial Differential Equations
Number Theory
Higher Geometry
Math. Investigation with Technology
Special Topics
Graduate, 6xxx (Intermittent)
Masters Oral Exam (6 cr. hrs.)
Course Prerequisites and Flow Chart
Value-Added
Testing
Cert. Math. 1
Value-Added
Testing
Precalculus
Port of Entry
Gov’t Oversight
Certification Testing
Calculus 1
Statistics
Number Theory
Algebra 1
Math. Reasoning
Linear Algebra
Cert. Math. 2
Calculus 2
Diff. Eq.’s
Probability
4xxx/5xxx by instructor consent only.
Value-Added
Testing
Certificate
of
Achievement
Calculus 3
Vector Analysis
Real Analysis 1
UTPB MATHEMATICS REORGANIZATION PLAN
Degree Plans of Mathematics Courses
Mathematics Major Course Degree Plan
1st Semester: Calculus 1
2nd Semester: Calculus 2
Mathematics Masters Degree Plan
3rd Semester: Calculus 3 & Diff. Eq.’s,
1st Semester: Algebra 2 or Analysis 2,
or Math. Reasoning
and one other 53xx
th
nd
4 Semester: Math. Reasoning, or
2 Semester: Analysis 2 or Algebra 2,
Calculus 3 & Diff. Eq.’s
and two other 53xx
th
rd
5 Semester: Two 33xx
3 Semester: three 53xx
6th Semester: Algebra 1 or Analysis 1,
4th Semester: Masters Oral Exam
and at least one 33xx
7th Semester: Analysis 1 or Algebra 1,
and at least one 43xx
8th Semester: At least two 43xx
Undergraduate Mathematics Degree Course Requirements (at least 120 cr. hrs.)
General Education (at least 44 cr. hrs.):
B.S. or B.A. Degree in Mathematics,
Engl. Comp. 1, 2
Major Field (at least 42 cr. hrs.):
Hist. 1, 2
Calculus 1, 2, 3
Lit.
Mathematical Reasoning
Math. 1, 2 (Calculus 1, 2)
Intro. to Differential Equations
Science w/ lab 1, 2 (8 cr. hrs.)
At least 3 33xx
Poli. Sci. 1, 2
Algebra 1
Visual or Perform. Arts
Real Analysis 1
Oral Comm.
At least 3 other 43xx courses
Soc. Sci.
B.S. or B.A. Degree in Mathematics,
Minor Field (at least 18 cr. hrs.):
The field must be chosen from those that
offer a B.S. or B.A. degree, respectively.
Consult with an advisor in the chosen
minor field for particular requirements.
Mathematics Minor and Masters Degree Course Requirements
Minor in Math. (at least 21 cr. hrs.):
Masters Degree in Mathematics
At least 12 hours at 1xxx or 2xxx (must
(at least 30 cr. hrs.):
be Calculus 1, 2, and 3 for B.S. degree
Algebra 2
seekers)
Real Analysis 2
Mathematical Reasoning
At least 6 other 53xx
At least 2 other 33xx or 43xx
Masters Oral Exam
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UTPB MATHEMATICS REORGANIZATION PLAN
Instructional Manpower Requirements Per Semester
1 Regular Faculty:
3 Regular Faculty:
Certification Mathematics Director
Precalc, …, or Calc 3
Precalc, …, or Calc 3 (Spr. Sem. only)
Math. Reasoning, or Intro to …
Math. Reasoning, or Intro to …
43xx, or 43xx/53xx
43xx, or 43xx/53xx
3-6 Graduate Student Assistants:
1 Visiting Professor (intermittent):
Certification Mathematics Instructors
Two courses, at least one at 43xx/53xx
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Notable Advantageous Features of the Plan
Course Condensation, Automation and Online Delivery at the Freshman Service
Level: Certification Mathematics
Focused Accountability and Institutional Structures for Value-Added Measures,
Standardized Testing, and Other Oversight Initiatives: Certification Mathematics,
Value-Added Testing and Certificates of Achievement
Reallignment of Non-Service Course Ratings and Prerequisites
Accomodation for Non-calculus Minor Track
Course Expansion and Enhancement at the Top Levels
B.S. and B.A. Degree Distinctions, Offerings
Overall Simplification of Course Requirements for Degrees and Minors in Math.
Masters Degree Program
Support for Graduate Student Teaching Assistants for Certification Mathematics
Support for a Visiting Professorship Position, Offerred Intermittently
Senior and Graduate Combined Courses
Online Delivery and Archiving of Traditional Courses at the Senior and Graduate
Combined Level
Implementation with the Current Number of Regular Faculty Positions (4) in
Mathematics
Enrollment Increases, A Goal Set by Present Administration
Notable Disadvantageous Features of the Plan
Substantial Activation Energy will be Necessary for Certification Mathematics
Development, Implementation, Etc.
Misconceptions and the Stigma of “Diploma Mills” Associated with Online
Degree Programs
Unknown Enrollment Support for Masters Program, Even with Online Course
Delivery, Funded Graduate Student Teaching Assistantships, and Senior and
Graduate Level Combined Courses.
Costs for Equipment and Support for Online Courses
Substantial Amount of Time Required for Full Implementation of the Plan
Unknown Sources of Funding for Graduate Student Instructorships and Visiting
Professorship
3
UTPB MATHEMATICS REORGANIZATION PLAN
Selected Course Descriptions
MATH 1310 Certification Mathematics 1. Mathematical content of administrative
oversight examinations required for teaching certification: Currently, ExCET
domains Algebra, Geometry and Mathematical Foundations. Meets Gen. Ed. college
Algebra Mathematics requirement. Prerequisites: Value-Added Testing placement.
MATH 1311 Certification Mathematics 2. Mathematical content of administrative
oversight examinations required for teaching certification: Currently, ExCET
domains Trigonometry, Analytic Geometry, Elementary Analysis, and Calculus and
Probability, Statistics, and Discrete Mathematics. Meets Gen. Ed. above college
Algebra Mathematics requirement. Prerequisites: Certification Mathematics 1, or
Value-Added Testing placement.
MATH 1432 Precalculus. Algebra, Algebraic Functions, Exponential and
Logarithmic Functions, Function Composition and Inverses, Trigonometry and
Trigonometric Functions in preparation for beginning a standard Calculus sequence
of study. Prerequisites: Two years of high school algebra, one year of high school
geometry and satisfactory score on placement examination.
MATH 1433 Calculus 1. Limits, derivatives and integrals for real-valued functions
of one real variable. Prerequisite: Precalculus, or satisfactory score on placement
examination.
MATH 1434 Calculus 2. Methods and applications of integration. Sequences, series,
power series, Taylor series. Prerequisite: Calculus 1.
MATH 2435 Calculus 3. Limits, derivatives and integrals for real vector-valued
functions of a real vector variable. Prerequisite: Calculus 2.
MATH 2300 Introduction to Statistics. Finite sample spaces and the descriptive and
inferential statistics on them: Measures of central tendency and dispersion,
hypotheses testing, correlation and regression, with case studies in business and the
social and behavioral sciences. Prerequisite: Satisfactory score on placement
examination.
MATH 2320 Introduction to Differential Equations. Ordinary differential equations
including power series, Laplace transform methods and systems of linear differential
equations with applications. Prerequisite: Calculus 2.
MATH 2399 Mathematical Reasoning. Tools for the transition away from
calculation toward advanced study of mathematics: The processes and formal
structures of mathematical reasoning and the basic concepts and methods involved in
mathematical constructions. Prerequisite: Satisfactory score on placement
examination.
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UTPB MATHEMATICS REORGANIZATION PLAN
MATH 3310 Introduction to Number Theory. Basic properties of integers, including
primes, unique factorization, divisibility congruences, Euler's phi function,
Diophantine equations and other selected topics. Prerequisite: Mathematical
Reasoning.
MATH 3320 Introduction to Vector Analysis. Topics include gradient, divergence,
curl, line and surface integrals, Green's, Stoke's and divergence theorems.
Prerequisite: Calculus 3.
MATH 3330 Introduction to Linear Algebra. Calculational and theoretical study of
systems of linear equations, matrices, vector spaces, linear independence, basis,
dimension, determinants, linear transformations and matrices, eigenvalues and
eigenvectors. Prerequisites: Calculus 2 and Mathematical Reasoning.
MATH 3340 Introduction to Probability. Axiomatic development of the theory of
probability and random variables, including combinatorial analysis of finite spaces,
independence and conditional probability, discrete and absolutely continuous
distributions, expectation, variation, correlation and covariance. Prerequisites:
Calculus 2 and Mathematical Reasoning.
MATH 4301 Algebra 1. The theory of groups, rings and fields, and the mappings on
them. Prerequisite: Mathematical Reasoning, or consent of instructor.
MATH 4302/5302 Algebra 2. Continuation of Algebra 1. Topics in the fundamental
theory of modern Abstract Algebra. Prerequisite: Consent of instructor.
MATH 4311 Real Analysis 1. The real number system and the elementary theory of
Calculus. Prerequisite: Mathematical Reasoning, or consent of instructor.
MATH 4312/5312 Real Analysis 2. Continuation of Real Analysis 1. Topics in the
elementary theory of modern Real Analysis. Prerequisite: Consent of instructor.
MATH 4369/5369 Mathematical Experimentation with Technology. Exploration of
topics and the formation of mathematical conjectures using modern computing
technology. Prerequisite: Consent of instructor.
MATH 6600 Masters Oral Exam. Specialized preparatory study in an active area of
Mathematical research. Prerequisite: Consent of instructor.
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