Faculty: Stephen Muir, Ph.D.
When one examines the job areas in which the largest amount of growth is expected over the next decade, the area of applied mathematics is quite notable. The ability to employ sophisticated mathematical tools and reasoning has become increasingly important in a number of seemingly different areas: prediction and rational decision making in finance, insurance, business, economic, and military strategy; sports analytics; bio- and social science research; weather and climate modeling; 3D computer graphics and animation; artificial intelligence for myriad applications ranging from manipulation of social media users, to smarter video games, to self-driving cars. Consequently, an increasing number of professions need to employ the skills of individuals with a strong background in core tools of applied mathematics. The applied mathematics major at the University of Providence is designed to guide motivated students step-by-step through the process of building a deep and broad foundation of core knowledge and skills in mathematics, statistics, and computer science to enable the student to create, implement, evaluate, and communicate complex mathematical models in a wide range of scholarly and industrial applications.
The Applied Math Major can serve as preparation for graduate study in mathematics, statistics, data science / analytics, operations research, or actuarial science, to name a few. It could also serve as a basis from which to seek 3+2 partnerships for a BS in engineering program.
The Applied Mathematics - Quantitative Business Concentration can serve as preparation for quantitatively rigorous MBA or Business PHD programs, or business analytics programs. It also includes the two courses focused towards actuarial exam preparation, and therefore it could also be a pathway to an actuarial or related career.
All courses will be available both in-person at the Great Falls campus and online through Moodle Collaborate, with the exception of laboratory science course electives.
Applied Mathematics Major - Common Learning Outcomes
In summary, the ability to create, implement, evaluate and present complex mathematical models, itemized as follows:
- A1. Proficiency with conceptual, analytical, and computational methods in calculus and calculus-based modeling.
- A2. General capability with programming syntax and structures that are relevant in computational mathematics, operations research, and data science.
- A3. Build a thorough foundation in probability theory.
- A4. With a deep understanding of the connection between algebraic and graphical representations, be able to curate and prepare visual representations of both theoretical objects/relationships and empirical data for the purposes of intuition building, visual analysis, and communication of results.
- A5. Gain extensive practice applying, combining, and innovating with problem solving strategies for both pure and applied problems, including problems for which specifically similar examples have not been provided.
Applied Mathematics Concentration - Specific Learning Outcomes
- A6. Develop and refine confident fluency in matrix algebra with theoretical rigor and familiarity with applications to scientific and economic modeling, statistical and data analysis applications, and vectorized coding.
- A7. Broad introduction to the use of ordinary differential equations in scientific, economic, and financial modeling, with mastery of foundational analytical and computational solution methods.
- A8. Build a toolbox of relevant statistical inference methods that is well-integrated into the foundation of probability theory.
- A9. With capstone coursework or undergraduate research, focus foundational studies around a concrete area of career or academic aspiration in contemporary applied mathematics.
Quantitative Business Concentration - Specific Learning Outcomes
In summary, the ability to implement and evaluate complex mathematical models that are particular to business, economics, and finance:
- QB1. Build and practice with a mathematical toolbox for strategic/rational decision making problems, using selected tools of probability and statistics, game theory, financial analysis, and machine learning.
- QB2. Gain conceptual, conversational, and moderate computational proficiency in micro- and macro- economic problems and models.
- QB3. Develop rigorous expertise with the mathematical theory of interest and its common financial applications.
- QB4. Familiarity with essential topics, principles, and methods in management, legal, accounting, and advertising for general business administration.
Minor Learning Outcomes:
- Analysis Concentration: A1, A5, and A7
- Statistics Concentration: A1, A3, and A8
- Math for Business and Finance Concentration: A1, QB1, QB3
Degree Requirements
Applied Mathematics (B.A.)
| Code | Title | Credits |
|---|---|---|
| CPS 161 | ELEMENTARY PROGRAMMING | 3 |
| CPS 165 | ADVANCED PROGRAMMING | 3 |
| CPS 301 | PHYS DES & IMPLM DATA MGMT SYS | 3 |
| CPS 403 | PRINCIPLES OF MACHINE LEARNING | 3 |
| MTH 177 | DISCRETE MATHEMATICS | 3 |
| MTH 241 | CALCULUS I | 4 |
| MTH 242 | CALCULUS II | 4 |
| MTH 243 | CALCULUS III | 4 |
| MTH 311 | MATHEMATICAL STATISTICS I - PROBABILITY THEORY | 3 |
| Specialized Concentration | 24-30 | |
| Total Credits Required: | 54-60 | |
Specialized Concentrations
Applied Mathematics Concentration
| Code | Title | Credits |
|---|---|---|
| Upper Division Applied Math Core | ||
| MTH 300 | LINEAR ALGEBRA | 3 |
| MTH 252 | STAT METHODS FOR THE SCIENCES | 3 |
| or MTH 312 | MATHEMATICAL STATISTICS II - STATISTICAL INFERENCE | |
| MTH 351 | DIFFERENTIAL EQUATIONS | 3 |
| MTH 400 | LINEAR ALGEBRA II | 3 |
| MTH 421 | MATHEMATICAL & NUMERICAL ANAYSIS | 3 |
| Electives | 9 | |
Choose from the following: | ||
| STAT METHODS FOR THE SCIENCES | ||
| MATHEMATICAL STATISTICS II - STATISTICAL INFERENCE * | ||
| FINANCIAL MATHEMATICS * | ||
| SPECIAL TOPICS - MATH | ||
| REAL ANALYSIS I * | ||
| REAL ANALYSIS II * | ||
| MODERN ALGEBRA * | ||
| GAME THEORY | ||
| SENIOR THESIS | ||
| CELL AND MOLECULAR BIOLOGY | ||
| GENETICS | ||
| Total Credits Required: | 24 | |
Quantitative Business Concentration
| Code | Title | Credits |
|---|---|---|
| ACC 201 | PRIN OF FINANCIAL ACCOUNTING | 3 |
| ECN 201 | MACROECONOMICS | 3 |
| ECN 202 | MICROECONOMICS | 3 |
| BUS 220 | COMMERCIAL LAW I | 3 |
| BUS 240 | LEADERSHIP & MANAGEMENT | 3 |
| BUS 241 | BUSINESS RESEARCH METHODS | 3 |
| BUS 260 | MARKETING | 3 |
| MTH 365 | FINANCIAL MATHEMATICS | 3 |
| BUS 400 | FINANCIAL ANALYSIS | 3 |
| MTH 406 | GAME THEORY | 3 |
| Total Credits Required: | 30 | |
Math for Business and Finance Minor
There is enough diversity in coursework within the two major concentrations to offer 3 targeted minor concentrations.
| Code | Title | Credits |
|---|---|---|
| MTH 106 | CONTEMPORARY MATHEMATICS | 3 |
| MTH 108 | ELEMENTARY STATISTICS | 3 |
| MTH 241 | CALCULUS I | 4 |
| MTH 242 | CALCULUS II | 4 |
| MTH 365 | FINANCIAL MATHEMATICS * | 3 |
| Total Credits Required: | 17 | |
Statistics Minor
Theoretical foundations and applied methods. Intended to make more competitive and well-rounded students going into graduate study and research-oriented careers in natural and social sciences.
| Code | Title | Credits |
|---|---|---|
| MTH 177 | DISCRETE MATHEMATICS | 3 |
| MTH 241 | CALCULUS I | 4 |
| MTH 242 | CALCULUS II | 4 |
| MTH 252 | STAT METHODS FOR THE SCIENCES | 3 |
| MTH 311 | MATHEMATICAL STATISTICS I - PROBABILITY THEORY | 3 |
| Total Credits Required: | 17 | |
Mathematical Analysis Minor
| Code | Title | Credits |
|---|---|---|
| MTH 241 | CALCULUS I | 4 |
| MTH 242 | CALCULUS II | 4 |
| MTH 243 | CALCULUS III | 4 |
| MTH 351 | DIFFERENTIAL EQUATIONS | 3 |
| Electives: | 6 | |
| Choose from the following: | ||
| DISCRETE MATHEMATICS | ||
| STAT METHODS FOR THE SCIENCES | ||
| LINEAR ALGEBRA | ||
| MATHEMATICAL STATISTICS I - PROBABILITY THEORY | ||
| MATHEMATICAL STATISTICS II - STATISTICAL INFERENCE * | ||
| FINANCIAL MATHEMATICS * | ||
| SPECIAL TOPICS - MATH | ||
| LINEAR ALGEBRA II | ||
| REAL ANALYSIS I * | ||
| REAL ANALYSIS II * | ||
| MODERN ALGEBRA * | ||
| GAME THEORY | ||
| MATHEMATICAL & NUMERICAL ANAYSIS | ||
| SENIOR THESIS | ||
| Total Credits Required: | 21 | |
| * | Courses offered on demand in directed study format. |