BS in Mathematics: Applied and Computational Mathematics Emphasis
(70 hours*)

Program Requirements    |    View MAP

1. Complete the following pre-core requirements before junior year.
MATH 112 : Calculus 1. (4:5:0)(Credit Hours:Lecture Hours:Lab Hours)

MATH 112 : Calculus 1. (4:5:0)(Credit Hours:Lecture Hours:Lab Hours)

OFFERED:	Honors also.
WHEN TAUGHT:	Fall; Winter; Spring; Summer
PREREQUISITE:	Math 110 and 111 or equivalent.
DESCRIPTION:	Differential and integral calculus: limits; continuity; the derivative and applications; extrema; the definite integral; fundamental theorem of calculus; L'Hopital's rule.

          : Honors Calculus 1.


Course Outcomes



MATH 113 : Calculus 2. (4:5:0)(Credit Hours:Lecture Hours:Lab Hours)

MATH 113 : Calculus 2. (4:5:0)(Credit Hours:Lecture Hours:Lab Hours)

OFFERED:	Honors also.
WHEN TAUGHT:	Fall; Winter; Spring; Summer
PREREQUISITE:	Math 112 or equivalent.
DESCRIPTION:	Techniques and applications of integration; sequences, series, convergence tests, power series; parametric equations; polar coordinates.


Course Outcomes



MATH 290 : Fundamentals of Mathematics. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)

MATH 290 : Fundamentals of Mathematics. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)

WHEN TAUGHT:	Fall; Winter
PREREQUISITE:	Math 112 or concurrent enrollment with instructor's consent.
DESCRIPTION:	Achieving maturity in mathematical communication. Introduction to mathematical proof; methods of proof; analysis of proof; induction; logical reasoning.


Course Outcomes



MATH 313 : Elementary Linear Algebra. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)

MATH 313 : Elementary Linear Algebra. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)

OFFERED:	Honors also.
WHEN TAUGHT:	Fall; Winter; Spring; Summer
PREREQUISITE:	MATH 112
RECOMMENDED:	Math 290.
DESCRIPTION:	Linear systems, matrices, vectors and vector spaces, linear transformations, determinants, inner product spaces, eigenvalues, and eigenvectors.

          : Honors Elementary Linear Algebra. (3:3:1)(Credit Hours:Lecture Hours:Lab Hours)


Course Outcomes



MATH 314 : Calculus of Several Variables. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)

MATH 314 : Calculus of Several Variables. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)

WHEN TAUGHT:	Fall; Winter; Spring; Summer
PREREQUISITE:	MATH 313
DESCRIPTION:	Partial differentiation, the Jacobian matrix, and integral theorems of vector calculus.


Course Outcomes



MATH 334 : Ordinary Differential Equations. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)

MATH 334 : Ordinary Differential Equations. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)

WHEN TAUGHT:	Fall; Winter; Spring; Summer
PREREQUISITE:	MATH 113 & MATH 313
DESCRIPTION:	Methods and theory of ordinary differential equations.


Course Outcomes



MATH 341 : Theory of Analysis 1. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)

MATH 341 : Theory of Analysis 1. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)

WHEN TAUGHT:	Fall; Winter
PREREQUISITE:	MATH 113 & MATH 290
DESCRIPTION:	Rigorous treatment of calculus of a single real variable: topology, order, completeness of real numbers; continuity, differentiability, integrability, and convergence of functions.


Course Outcomes



C S 142 : Introduction to Computer Programming. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)

C S 142 : Introduction to Computer Programming. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)

WHEN TAUGHT:	Fall; Winter; Spring
PREREQUISITE:	Knowledge of algebra.
DESCRIPTION:	Introduction to object-oriented program design and development. Principles of algorithm formulation and implementation.


Course Outcomes



2. Complete the following core requirements during fall semester, junior year:
   MATH 320 : Computation and Optimization 1. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)
   
   MATH 320 : Computation and Optimization 1. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)
   
   WHEN TAUGHT:	Fall
   PREREQUISITE:	MATH 290 & MATH 313 & MATH 314; concurrent enrollment in Math 321, 334, 344.
   DESCRIPTION:	A treatment of algorithms used to solve these problems. Topics include complexity and data, approximation theory, recursive algorithms, linear optimization, unconstrained optimization, constrained optimization, global optimization.
   
   
   Course Outcomes
   
   
   
   MATH 321 : Computation and Optimization 1 Laboratory. (1:0:2)(Credit Hours:Lecture Hours:Lab Hours)
   
   MATH 321 : Computation and Optimization 1 Laboratory. (1:0:2)(Credit Hours:Lecture Hours:Lab Hours)
   
   WHEN TAUGHT:	Fall
   PREREQUISITE:	Concurrent enrollment in Math 320, 345.
   DESCRIPTION:	Programming algorithms and using functions to implement the optimization algorithms taught in Math 320. Applications presented. Developing models and applying results of computations to the application domain.
   
   
   Course Outcomes
   
   
   
   MATH 344 : Linear and Nonlinear Analysis 1. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)
   
   MATH 344 : Linear and Nonlinear Analysis 1. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)
   
   WHEN TAUGHT:	Fall
   PREREQUISITE:	MATH 290 & MATH 313 & MATH 314; concurrent enrollment in Math 334, 345.
   DESCRIPTION:	Development of theory of vector spaces, linear maps, inner product spaces, spectral theory, metric space topology, differentiation, contraction mappings and convex analysis.
   
   
   Course Outcomes
   
   
   
   MATH 345 : Linear and Nonlinear Analysis 1 Laboratory. (1:0:2)(Credit Hours:Lecture Hours:Lab Hours)
   
   MATH 345 : Linear and Nonlinear Analysis 1 Laboratory. (1:0:2)(Credit Hours:Lecture Hours:Lab Hours)
   
   WHEN TAUGHT:	Fall
   PREREQUISITE:	Concurrent enrollment in Math 344.
   DESCRIPTION:	Programming algorithms to implement the key mathematical methods taught in Math 344. Applications presented. Developing models and applying results of computations to the application domain.
   
   
   Course Outcomes
   
   
   
3. Complete the following core requirements during winter semester, junior year:
   MATH 322 : Computation and Optimization 2. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)
   
   MATH 322 : Computation and Optimization 2. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)
   
   WHEN TAUGHT:	Winter
   PREREQUISITE:	MATH 320; concurrent enrollment in Math 323, 346.
   DESCRIPTION:	Algorithms used to solve dynamic programming problems and advanced computing problems. Topics include finite-horizon and infinite-horizon dynamic programming, discrete transforms, compressed sensing, heuristics, branch and bound, conditioning and stability.
   
   
   Course Outcomes
   
   
   
   MATH 323 : Computation and Optimization 2 Laboratory. (1:0:2)(Credit Hours:Lecture Hours:Lab Hours)
   
   MATH 323 : Computation and Optimization 2 Laboratory. (1:0:2)(Credit Hours:Lecture Hours:Lab Hours)
   
   WHEN TAUGHT:	Winter
   PREREQUISITE:	MATH 321; concurrent enrollment in Math 322, 347.
   DESCRIPTION:	Using existing software and writing code for algorithms taught in Math 322. Applications presented. Developing models and applying results to the application domain.
   
   
   Course Outcomes
   
   
   
   MATH 346 : Linear and Nonlinear Analysis 2. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)
   
   MATH 346 : Linear and Nonlinear Analysis 2. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)
   
   WHEN TAUGHT:	Winter
   PREREQUISITE:	MATH 344; concurrent enrollment in Math 347.
   DESCRIPTION:	Theory of Riemann-Darboux integration, calculus on curves and surfaces, complex integration, spectral calculus, generalized inverses of matrices, basic matrix perturbation theory, groups of permutations and matrices. Time permitting, exterior calculus and differential forms.
   
   
   Course Outcomes
   
   
   
   MATH 347 : Linear and Nonlinear Analysis 2 Laboratory. (1:0:2)(Credit Hours:Lecture Hours:Lab Hours)
   
   MATH 347 : Linear and Nonlinear Analysis 2 Laboratory. (1:0:2)(Credit Hours:Lecture Hours:Lab Hours)
   
   WHEN TAUGHT:	Winter
   PREREQUISITE:	MATH 345; concurrent enrollment in Math 346.
   DESCRIPTION:	Programming algorithms and using functions to implement the mathematical methods taught in Math 346. Applications presented. Developing models and applying results of computations to the application domain.
   
   
   Course Outcomes
   
   
   
4. Complete the following core requirements during spring/summer terms, junior year:
   MATH 402 : Probability and Statistics 1. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)
   
   MATH 402 : Probability and Statistics 1. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)
   
   WHEN TAUGHT:	Summer
   PREREQUISITE:	MATH 322 & MATH 346; concurrent enrollment in Math 403.
   DESCRIPTION:	Theory of probability and stochastic processes, emphasizing topics used in applications. Random spaces and variables, probability distributions, limit theorems, martingales, diffusion, Markov, Poisson and queuing processes, renewal theory, and information theory.
   
   
   Course Outcomes
   
   
   
   MATH 403 : Probability and Statistics 1 Laboratory. (1:0:2)(Credit Hours:Lecture Hours:Lab Hours)
   
   MATH 403 : Probability and Statistics 1 Laboratory. (1:0:2)(Credit Hours:Lecture Hours:Lab Hours)
   
   WHEN TAUGHT:	Summer
   PREREQUISITE:	C S 142 & MATH 323 & MATH 347; concurrent enrollment in Math 402.
   DESCRIPTION:	Using and developing algorithms for the content of Math 402; developing I/O wrappers for numerical libraries. Applications presented. Developing models and applying results of computations.
   
   
   Course Outcomes
   
   
   
   MATH 436 : Differential and Integral Equations 1. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)
   
   MATH 436 : Differential and Integral Equations 1. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)
   
   WHEN TAUGHT:	Summer
   PREREQUISITE:	MATH 322 & MATH 341 & MATH 346; concurrent enrollment in Math 437.
   DESCRIPTION:	Theory and applicatiions of dynamic systems and partial differential equations. Topics include dynamic systems; bifurcation theory; control theory; hyperbolic, parabolic, and elliptic partial differential equations; commonly-used algorithms.
   
   
   Course Outcomes
   
   
   
   MATH 437 : Differential and Integral Equations 1 Laboratory. (1:0:2)(Credit Hours:Lecture Hours:Lab Hours)
   
   MATH 437 : Differential and Integral Equations 1 Laboratory. (1:0:2)(Credit Hours:Lecture Hours:Lab Hours)
   
   WHEN TAUGHT:	Summer
   PREREQUISITE:	C S 142 & MATH 323 & MATH 347; concurrent enrollment in Math 346.
   DESCRIPTION:	Using and developing software to implement the content of Math 436. Developing models and applying results of computations to several application domains. Introduction to parallel computation.
   
   
   Course Outcomes
   
   
   
5. Complete the following core requirements during winter semester, senior year:
   MATH 404 : Probability and Statistics 2. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)
   
   MATH 404 : Probability and Statistics 2. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)
   
   WHEN TAUGHT:	Winter
   PREREQUISITE:	MATH 402; concurrent enrollment in Math 405.
   DESCRIPTION:	First course in mathematical statistics, focusing on mathematical aspects. Topics include estimation, inference, analysis of variance, regression, multivariate statistics, Bayesian statistics, state estimation, Kalman filtering, time series, GARCH models.
   
   
   Course Outcomes
   
   
   
   MATH 405 : Probability and Statistics 2 Laboratory. (1:0:2)(Credit Hours:Lecture Hours:Lab Hours)
   
   MATH 405 : Probability and Statistics 2 Laboratory. (1:0:2)(Credit Hours:Lecture Hours:Lab Hours)
   
   WHEN TAUGHT:	Winter
   PREREQUISITE:	MATH 403; concurrent enrollment in Math 404.
   DESCRIPTION:	Using and developing software to implement the content of Math 404 and handle large data sets. Applications presented. Designing and executing statistical tests and applying computations to application domains.
   
   
   Course Outcomes
   
   
   
   MATH 438 : Differential and Integral Equations 2. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)
   
   MATH 438 : Differential and Integral Equations 2. (3:3:0)(Credit Hours:Lecture Hours:Lab Hours)
   
   WHEN TAUGHT:	Winter
   PREREQUISITE:	MATH 402 & MATH 436; concurrent enrollment in Math 404, 439.
   DESCRIPTION:	Introduction to integral equations, calculus of variations, stochastic differential equatons, optimal stochastic control; common algorithms used for these systems.
   
   
   Course Outcomes
   
   
   
   MATH 439 : Differential and Integral Equations 2 Laboratory. (1:0:2)(Credit Hours:Lecture Hours:Lab Hours)
   
   MATH 439 : Differential and Integral Equations 2 Laboratory. (1:0:2)(Credit Hours:Lecture Hours:Lab Hours)
   
   WHEN TAUGHT:	Winter
   PREREQUISITE:	MATH 437; concurrent enrollment in Math 405, 438.
   DESCRIPTION:	Using and developing software for problems in the calculus of variations, stochastic differential equations, and stochastic optimal control. Developing models and applying the results of computations to several application domains.
   
   
   Course Outcomes
   
   
   
6. Students are required to complete a concentration in an area to which the mathematical and computational tools that they are learning can be applied. The list of the Approved Concentrations is found at http://math.byu.edu/concentrations.

Note: The core courses for the junior year listed above will be offered for the first time in the 2013-2014 academic year.

*Hours include courses that may fulfill university core requirements.

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