Courses | Mathematics, B.S.

Summary

Below are some of the courses you’ll have an opportunity to take as a student in this program. Note: This list is intended to give you a quick glimpse into the program’s academic offerings, and should not be used as a guide for course selection or academic advising. For official program requirements see catalog for details.

Major Courses

Introduction to computer hardware and software. Problem solving methods. Elementary concepts of algorithm development. C++ programming.

Limits, differentiation and integration of rational and trigonometric functions, with applications.

Differentiation and integration of logarithmic, exponential and inverse trigonometric functions; various methods of integration; infinite sequences and series; parametric equations, polar coordinates.

Set theory, Cartesian products, equivalence relations, images and inverse images, induction, recursions, inequalities, and field axioms. Emphasis on how to discover, write and present proofs.

Functions of two and three variables, partial differentiation, multiple integration, curves and surfaces in three dimensional space.

Topics from matrices, determinants, linear transformations and vector spaces.

The real number system, elementary topological concepts in Cartesian spaces, convergence, continuity, derivatives and integrals.

Introduction to abstract algebra with topics from elementary ring, field and group theories. Emphasis on ring of integers, congruences, polynomial domains, permutation groups.

Reading of material in a special topic. Colloquium participation. Writing and oral presentation of a research paper.


Concentrations

Pure Mathematics

See course catalog for details.

Applied Mathematics

Functions of one variable, approximate numerical solutions of non-linear equations and systems of linear equations, interpolation theory, numerical differentiation and integration, numerical solutions of ordinary differential equations.

Samples spaces, axioms and elementary theorems of probability, combinatorics, independence, conditional probability, Bayes' Theorem, one and higher dimensional random variables, special and multivariate distributions.

Estimation: consistency, unbiasedness, maximum likelihood, confidence intervals. Hypothesis-testing; type I and II errors, likelihood ratio tests, test for means and variances; regression and correlation, Chi-square tests, decision theory, nonparametric statistics; application of statistical methods.

Mathematical foundations of model building, optimization, linear programming models, game theoretic models.

First order differential equations, second order linear differential equations, power series solutions, Laplace transforms, systems of first order linear equations.

Complex variables, analytic functions, complex integral theorems, power series, conformal mappings.

Computer Science

Linear lists, strings, arrays and orthogonal lists; graphs, trees, binary trees, multi-linked structures, searching and sorting techniques, dynamic storage allocation; applications.

Fundamentals of digital logic and the architecture of modern computer systems, machine level representation of data, memory system organization, structure of machine languages, assembly language programming.

Various types of algorithms, analytic techniques for the determination of algorithmic efficiency, NP-complete problems, complexity hierarchies, and intractable problems.

Functions of one variable, approximate numerical solutions of non-linear equations and systems of linear equations, interpolation theory, numerical differentiation and integration, numerical solutions of ordinary differential equations.

Samples spaces, axioms and elementary theorems of probability, combinatorics, independence, conditional probability, Bayes' Theorem, one and higher dimensional random variables, special and multivariate distributions.

Estimation: consistency, unbiasedness, maximum likelihood, confidence intervals. Hypothesis-testing; type I and II errors, likelihood ratio tests, test for means and variances; regression and correlation, Chi-square tests, decision theory, nonparametric statistics; application of statistical methods.

Mathematical foundations of model building, optimization, linear programming models, game theoretic models.

Secondary Instruction

This course examines the structure and function of the school, foundations of education, qualities required for teacher effectiveness, and contemporary issues in education. A 25-hour fieldwork practicum component is required. Successful completion of this course constitutes one of the requirements for admission to the Teacher Preparation Program. CBEST must be taken during this course.

Application of psychological principles to the education process, role of the teacher and learner, human growth and development, learning styles, motivation, memory, transfer of learning, measurement and evaluation, research and experimentation in learning theory.

Survey of the theories, programs, and instructional practices for English language development, including first and second language acquisition and individual factors affecting language acquisition. Strategies for the application of theory to classroom practice and instruction in content area literacy are emphasized. Principles of educational equity, diversity, and cultural and linguistic responsiveness are examined.

Methods and materials for teaching reading through content areas in secondary schools; attention to reading techniques, testing, and individualization.

During interrelated activities in program coursework and fieldwork, Single Subject candidates relate the Common Core and the state-adopted K-12 academic content standards for candidates in their specific subject area to major concepts and principles in their discipline, including planning, organizing, and implementing effective instruction (Grades 7-12).

Single Subject Pedagogy - Art: 
During interrelated activities in program coursework and fieldwork, Single Subject Art candidates learn, understand and use content-specific teaching strategies for achieving the fundamental goals of the state-adopted K-12 academic content standards for students in Art (Grades 7-12).

Single Subject Pedagogy - English: During interrelated activities in program coursework and fieldwork, Single Subject English candidates learn, understand and use content-specific teaching strategies for achieving the fundamental goals of the state-adopted K-12 academic content standards for students in English (Grades 7-12).

Single Subject Pedagogy - Methods of Teaching Spanish as a Foreign Language: During interrelated activities in program coursework and fieldwork, Single Subject Modern Language candidates learn, understand, and use specific teaching strategies and activities for achieving the fundamental goals of the state-adopted K-12 Foreign Language Framework and Student Academic Content Standards for students learning Spanish (Grades 7-12).

Single Subject Pedagogy - Health Science: 
During interrelated activities in program coursework and fieldwork, Single Subject Health Science candidates learn, understand and use content-specific teaching strategies for achieving the fundamental goals of the state-adopted K-12 academic content standards for students in Health Science (Grades 7-12).

Single Subject Pedagogy - History/Social Science: During interrelated activities in program coursework and fieldwork, Single Subject History/Social Science candidates learn, understand and use content-specific teaching strategies for achieving the fundamental goals of the K-12 state-adopted academic content standards for History/Social Science (Grades 7-12).

Single Subject Pedagogy - Mathematics: During interrelated activities in program coursework and fieldwork, Single Subject Mathematics candidates acquire a deep understanding of the interrelated components of a balanced program of mathematics instruction: computational and procedural skills; conceptual understanding of mathematics; and problem solving skills in mathematics, and acquire pedagogical skills that assist students in learning K-12 state-adopted academic content standards for Mathematics (Grades 7-12).

Single Subject Pedagogy - Physical Education: During interrelated activities in program coursework and fieldwork, Single Subject Physical Education candidates learn, understand and use content-specific teaching strategies for helping students in learning K-12 state-adopted academic content standards for Physical Education (Grades 7-12).

Single Subject Pedagogy - Science: During interrelated activities in program coursework and fieldwork, Single Subject Science candidates relate the state-adopted K-12 academic content standards for students in Science (Grades 7-12) to major concepts, principles and investigations in the science disciplines, including planning, organizing, and implementing effective instruction.

 

Secondary school curriculum, assessment, classroom management and teaching methods as they apply to the content areas in secondary school settings.

A 60-hour fieldwork requirement to support the practical application of LEDU 436 Secondary Curriculum content. Candidates will design and teach several classroom lessons in local secondary schools.

Prepares the student for biostatistical application essential to practice in evidence-based professions. Content includes: descriptive statistics; probability theory and rules; discrete and continuous probability distributions; sampling distributions; confidence intervals; hypothesis testing; experimental design; ANOVA; linear and multiple regression; contingency table analysis; non-parametrics; survival analysis; discussion of the use of statistics in journal articles.

Samples spaces, axioms and elementary theorems of probability, combinatorics, independence, conditional probability, Bayes' Theorem, one and higher dimensional random variables, special and multivariate distributions.

Estimation: consistency, unbiasedness, maximum likelihood, confidence intervals. Hypothesis-testing; type I and II errors, likelihood ratio tests, test for means and variances; regression and correlation, Chi-square tests, decision theory, nonparametric statistics; application of statistical methods.

Theorems of Pythagoras, incenters, circumcenters, circles, Euler line, Fermat center. Compass constructions. Solid geometry. Spherical geometry of arcs. Coordinate geometry.

The history of mathematics from Euclid through the 19th century as seen by exploring developments in number theory including congruences, Diophantine equations, divisibility, theorems of Fermat and Wilson, primitive roots, indices, quadratic reciprocity and the distribution of prime numbers.