# Named options

The **Mathematics Major** offers a variety of **Named Options** which allow a major to focus on those topics in mathematics which have a strong relationship to a particular other area of study. This page describes those options and highlights topics and courses worthy of special consideration.

NOTES:

1) Be aware that the below describes initial collections of courses and ideas worth considering which fulfill major requirements. **Please refer to the guide for all possible courses which can be applied to your named option plan and meet with an advisor in order to construct a course plan which works best for you.**

2) Note that course suggestions **may have prerequisites**.

3) Courses offered by departments/schools besides mathematics may have **restricted enrollment**.

## Contents

## General Requirements and notes for all Named Options

In general, all named option programs will have the following requirements:

1) A course in linear algebra (MATH 320, 340, 341, or 375)

2) An intermediate level "transition" course or sequence: MATH 321/2, 341, 421, or 467

3) A minimum of two advanced MATH courses (Numbered 500 and above).

4) A minimum of 21 credits in MATH from no fewer than seven courses.

Any additional course/credit/level requirements are specific to each Named Option and students should refer to the guide for complete descriptions.

## MATHEMATICS FOR DATA, STATISTICS, AND RISK ANALYSIS

For students interested in mathematics inspired by or used in the fields of Statistics, Data Science, Actuarial Science, Bio-Statistics, and many others.

Students interested in this option should choose coursework focused on linear algebra, probability, statistics, analysis, and computational mathematics.

*Linear Algebra*:
MATH 320, 340, 341, 375, 540

*Probability*:
MATH 309, 431, 531, 535

*Statistics*:
MATH 310

*Analysis*:
MATH 321 and 322, 421, 521

*Numerical Methods*:
MATH 514

*Data/Risk/Stat Core*:
ACT SCI 303 or
(STAT 333 and STAT 424) or
(STAT 340 and STAT 424)

## MATHEMATICS FOR THE PHYSICAL AND BIOLOGICAL SCIENCES

Mathematics and the natural sciences have had a long and fruitful relationship since the dawn of humanity. This named option may be of interest to any mathematics student with a strong interest in physics, chemistry, biology, and most areas of engineering.

Students interested in this named option should focus on linear algebra, differential equations, geometry, and analysis.

*Linear Algebra and Algebra*:
MATH 320, 340, 341, 375, 540, 541

*Differential Equations*:
MATH 319, 320, 376, 519, 619

*Geometry and Topology*:
MATH 551, 561

*Real and Complex Analysis*:
MATH 321 and 322, 421, 514, 521, 623

*Other topics*:
MATH 531

*Core Natural Science*:
Physics 247/207/201/EMA 201 and Physics 248/208/202

## MATHEMATICS FOR SECONDARY EDUCATION

This option is designed with input from our own School of Education to cover all core areas of mathematics expected of a secondary instructor in the context of a mathematics major.

*Linear Algebra*:
MATH 320, 340, 341, 375

*Analysis*: MATH 421, 521

*Algebra*:
MATH 540, 541

*Probability/Combinatorics*:
MATH 309, 431, 475, 531

*Statistics*:
STAT 301, 302, 312, 324, MATH 310, ECON 310

*History of Mathematics*:
MATH 473

*Geometry*:
MATH 461

*Capstone*:
MATH 471

## MATHEMATICS FOR ECONOMICS AND FINANCE

This option is inspired by interesting problems and applications in certain areas of business and economics (operations management, financial modeling, market behavior, and so on).

The mathematics is built around analysis, which allows us to link together different mathematical areas. For example: the theory of differential equations, which we use to model systems in order to make specific predictions on outcomes, with the theory of probability, which we use to model systems which have a variety of unknown outcomes. In addition to these topics, we recommend a strong background in linear algebra .

*Linear Algebra*:
MATH 320, 340, 341, 375, 443, 540

*Differential Equations*: MATH 319, 320, 376, 415

*Probability and Statistics*: MATH 309, 431, 310, 531

*Analysis*:
MATH 321-2 sequence, 421, 521(this is a required class for this program).

*Introductory Econ/Finance Sequences*:
Micro (ECON 301 or 311) and Macroeconomics (ECON 302 or 312)

or

FIN 300 and 320

## MATHEMATICS FOR PROGRAMMING AND COMPUTING

The areas of mathematics of interest here are often lazily grouped as "discrete" and include topics in algebra, probability, and number theory. However, analysis plays an extremely strong role in unexpected ways. For example: An iterative system which builds successive approximations can be thought of as a sequence. So questions about how well that system works can be restated as questions about if the sequence has a limit, how quickly the sequence converges to that limit, and so on.

*Algebra*: MATH 320, 340, 341, 375, 540, 541

*Analysis*: MATH 321-2, 421, 514, 521

*Probability*: MATH 309, 431, 531, 535

* Number Theory*: MATH 467, 567

Other areas of interest include combinatorics (MATH 475) and logic (MATH 571).

Students should also aim to complete the standard introductory programming sequence: CS 300 and 400.