Curriculum | Mathematics Major | Concordia University Irvine

Mathematics

Curriculum

School of Arts and Sciences

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Curriculum

  • Mathematics Major
  • 44 Units
  • MTH 265: Introduction to Statistics
  • 3

As a basic statistics course applicable to education, business, and the hard sciences, this course will include topics such as descriptive statistics, the normal, binomial, F-, and Chi-squared distributions, and hypothesis testing. Optional topics might include additional non-parametric tests and ANOVA. A TI-83 graphing calculator or Microsoft Excel is required.

  • MTH 271: Calculus 1
  • 5

This course will study differential and integral calculus with applications including an emphasis on using calculus to solve problems. Lab time is included in the schedule. A graphing calculator is expected.

  • MTH 272: Calculus II
  • 5

A continuation of MTH 271, this course will include a study of integral calculus with and emphasis on the definite integral, transcendental, parametric, and polar-functions along with their derivatives and integrals, series, and sequences, and an introduction to differential equations. A graphing calculator is expected along with the ability to use appropriate computer software. Lab time is included in the schedule. Prerequisite: MTH 271 or acceptable AP examination credit.

  • MTH 295: Mathematical Notation and Proof
  • 3

This course will introduce standard mathematical notation, methods, truth tables, and principles of symbolic logic for use in determining the validity of arguments, dealing with proper notation and structure in mathematical proofs including direct and indirect proofs, mathematical induction, and construction of counter-examples. Application will be made to a field of mathematics such as set theory, algebra, or geometry.

  • MTH 371: Linear Algebra
  • 3

This course will study properties of matrix arithmetic, systems of linear equations, determinants, vector spaces, linear transformations, diagonalization, inner products, and applications of these topics. Prerequisite: Mth 272 or appropriate advanced placement examination grade.

  • MTH 373: Calculus 3
  • 4

As a continuation of MTH 272, this course will include the study of vector calculus, three-dimensional calculus, partial derivatives, multiple integrals, differential calculus, and other selected topics in vector calculus. Prerequisite: MTH 272 or appropriate advanced placement (AP) examination grade.

  • MTH 387: Theory of Probability
  • 3

This course will look at the probability and combinatorics; discrete and continuous random variables; the normal, gamma, Chi-square, Poisson, and binomial distributions with applications. Offered alternate years.

  • MTH 473: Modern Algebra
  • 3

This course will study the properties and operations within groups, rings, integral domains, fields, normal subgroups, quotient groups, homomorphism's, and isomorphism's. Prerequisite: MTH 373. Offered alternate years.

  • MTH 484: Differential Equations
  • 3

Classification of differential equations is covered. First order equations, exact differentials, integrating factors, higher order differential equations, method of undetermined coefficients, variation of parameters, operator methods, and solution by infinite series and Laplace transformations are taught. Prerequisite: MTH 373 or approval of instructor.

  • MTH 489: Real Analysis
  • 3

This course will introduce the topics of real analysis by studying the topology of Rn, continuity, differentiability, integration, and how these topics are related. Included will be proofs of the Heine-Borel and Bolzano-Weierstrass theorems, the intermediate value and mean value theorem, as well as the fundamental theorem of calculus. Prerequisites: MTH 295 and MTH 373. Offered alternate years.

  • MTH 495: Topics in Mathematics - Review
  • 1.5

As the first of two (2) capstone courses for all mathematics majors, students will meet as a group once per week to review competencies in the major, take group-wide assessments, and complete a preliminary research abstract on a topic of their choice as they work with a faculty mentor followed by a short presentation to their peers and faculty regarding their preliminary findings for reaction and feedback. Prerequisite: senior standing.

  • MTH 496: Topics in Mathematics - Final
  • 1.5

As the second of two (2) capstone courses for all mathematics majors, students, working with a faculty mentor, will complete their research from MTH 495 on a written project and present their findings to a committee of peers and faculty. Inclusion of the research project in the President's Academic Showcase for Undergraduate Research is encouraged. Prerequisite: Senior standing.

  • Choose two of the following courses:
  • MTH 376: Discrete Mathematics
  • 3

This course will include the study of relations and functions, graph theory, counting principles and combinatorics, set theory, Boolean algebra, code theory, linear programming, and other selected topics. Offered alternate years.

  • MTH 380: Modern Geometry
  • 3

This course will provide a general study of deductive systems of geometry including Euclidean, projective, finite, and other non-Euclidean geometries. Offered alternate years.

  • MTH 388: Mathematical Statistics
  • 3

A continuation of MTH 387, this course will cover various multivariate probability distributions, bias and unbiased estimators, Least Square estimation, ANOVA , Block Designs, and a revisit of hypothesis testing and a study of nonparametric statistics. Prerequisite: MTH 387. Offered alternate years.

  • MTH 420: Number Theory
  • 3

This course will provide a developmental study of natural numbers and the integers including mathematical induction, prime numbers, divisibility, congruence, and Diophantine along with selected theorems and applications of Fermat, Euler, and Gauss as well as modern applications of number theory. Prerequisite: MTH 295 or approval of instructor. Offered alternate years.

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