# Applied and Computational Mathematics, B.S.

The Department offers a B.S. in Applied and Computational Mathematics. Within this program there are four tracks; besides the standard track, there is one specialization (in Mathematical Biology) and two concentrations (in Mathematical Finance and Data Science). In addition, the Department offers a B.S. in Mathematics (which focuses more on topics in pure mathematics) and minors in Mathematics and Mathematics for Biology.

Undergraduate mathematics courses are of several kinds: courses preparatory to advanced work in mathematics, the exact sciences, and engineering; courses for students of the social and biological sciences; and courses for liberal arts students and those planning to enter the teaching field.

Students may be admitted to the Applied and Computational Mathematics major upon entering the University as freshmen, via change of major, or as transfer students from other colleges and universities. Information about change of major policies is available in the Physical Sciences Student Affairs Office and at the UCI Change of Major Criteria website. For transfer student admission, preference will be given to junior-level applicants with the highest grades overall and who have satisfactorily completed the required coursework of one year of approved calculus. Additional course work in multivariable calculus, linear algebra, and differential equations is strongly recommended.

###### All students must meet the University Requirements.

School Requirements: None.

##### Core Requirements for all Applied and Computational Mathematics Majors

Lower-Division Requirements: | |

A. Complete the following: | |

MATH 2A- 2B | Single-Variable Calculus I and Single-Variable Calculus II |

MATH 2D | Multivariable Calculus I |

MATH 2E | Multivariable Calculus II |

MATH 3A | Introduction to Linear Algebra |

MATH 3D | Elementary Differential Equations |

MATH 9 | Introduction to Programming for Numerical Analysis |

MATH 13 | Introduction to Abstract Mathematics |

Upper-Division Requirements: | |

A. Complete the following: | |

MATH 105A- 105LA | Numerical Analysis I and Numerical Analysis Laboratory |

MATH 105B- 105LB | Numerical Analysis II and Numerical Analysis Laboratory |

MATH 121A- 121B | Linear Algebra I and Linear Algebra II |

MATH 130A | Probability I |

MATH 140A- 140B | Elementary Analysis I and Elementary Analysis II |

#### Requirements for the Applied and Computational Mathematics Major

Core requirements for all Applied and Computational Mathematics majors plus: | |

Lower-Division Requirements: | |

A. Select three lower-division courses from the following: | |

From DNA to Organisms and DNA to Organisms - Introduction to Biology Research | |

From Organisms to Ecosystems and Organisms to Ecosystems - Introduction to Biology Research Analysis | |

Genetics | |

General Chemistry | |

General Chemistry | |

General Chemistry | |

Introduction to Programming for Data Science | |

Classical Physics | |

Classical Physics | |

Classical Physics | |

Basic Statistics | |

Upper-Division Requirements: | |

A. Complete: | |

MATH 112A- 112B | Introduction to Partial Differential Equations and Applications I and Introduction to Partial Differential Equations and Applications II |

MATH 115 | Mathematical Modeling |

B. Select three additional upper-division MATH courses from the following: | |

Numerical Differential Equations and Numerical Differential Equations Laboratory | |

Optimization I | |

Optimization II | |

Introduction to Partial Differential Equations and Applications III | |

Mathematical Modeling in Biology I | |

Mathematical Modeling in Biology II | |

Mathematical Modeling | |

Dynamical Systems | |

The Theory of Differential Equations | |

Introduction to Abstract Algebra: Groups | |

Probability II | |

Stochastic Processes | |

Fixed Income | |

Mathematics of Financial Derivatives | |

Analysis in Several Variables | |

Complex Analysis | |

Mathematics of Finance | |

Mathematical Machine Learning | |

C. Select two 4-unit upper-division courses in an area outside of mathematics from the below list or obtain advanced approval from an Applied and Computational Mathematics advisor for courses outside of this list: | |

Introduction to Data Management | |

Design and Analysis of Algorithms | |

Introduction to Artificial Intelligence | |

Neural Networks and Deep Learning | |

Machine Learning and Data-Mining | |

Introduction to Computational Biology | |

Intermediate Economics I | |

Intermediate Quantitative Economics I | |

Intermediate Quantitative Economics II | |

Management Science | |

Introduction to Marketing | |

Introduction to Management Information Systems | |

Introduction to Logic | |

Introduction to Set Theory and Mathematical Reasoning | |

Metalogic | |

Computational Methods | |

Classical Mechanics | |

Classical Mechanics | |

Relativity and Black Holes | |

Mathematical Physics | |

Mathematical Physics | |

Statistical Methods for Data Analysis I | |

Statistical Methods for Data Analysis II | |

Statistical Methods for Data Analysis III | |

Introduction to Probability and Statistics II |

##### Sample Program — Applied and Computational Mathematics

Freshman | ||
---|---|---|

Fall | Winter | Spring |

MATH 2A | MATH 2B | MATH 2D |

PHYSICS 7C or CHEM 1A | PHYSICS 7D or CHEM 1B | PHYSICS 7E or CHEM 1C |

General Education/Elective | General Education/Elective | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

Sophomore | ||

Fall | Winter | Spring |

MATH 2E | MATH 3A | MATH 3D |

MATH 9 | MATH 13 | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

Junior | ||

Fall | Winter | Spring |

MATH 105A- 105LA | MATH 105B- 105LB | MATH 121B |

MATH 130A | MATH 121A | Upper-Division Math Elective |

General Education/Elective | Upper-Division Math Elective | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

Senior | ||

Fall | Winter | Spring |

MATH 112A | MATH 112B | MATH 115 |

MATH 140A | MATH 140B | Non-Math Elective |

Upper-Division Math Elective | Non-Math Elective | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

The Applied and Computational Mathematics major offers two concentrations and one specialization. Note that all require the completion of an application and an interview with the faculty advisor for that concentration or specialization. **Admission into a concentration or specialization is not guaranteed.** Students must complete the basic "Core" requirements for the B.S. in Applied and Computational Mathematics along with the lower- and upper-division requirements specified for each concentration and specialization. Students choosing to specialize or concentrate can only do so with a single specialization/concentration.

#### Requirements for Applied and Computational Mathematics Major with a Concentration in Data Science

Admission to this concentration requires approval in advance by the Mathematics Department. Students need a GPA of 3.0 in all lower-division and upper-division MATH courses to be admitted to the concentration. Before applying, students should have finished all lower-division requirements for the Data Science concentration. The admissions process begins with completing a Data Science concentration advising form and includes an interview with the Department's advisor for the concentration. This approval should be applied for no later than the end of the junior year.

Core requirements for all Mathematics majors plus: | |

Lower-Division Requirements: | |

A. Complete: | |

MATH 10 | Introduction to Programming for Data Science |

STATS 7 | Basic Statistics |

PHYSICS 7C | Classical Physics |

Upper-Division Requirements: | |

A. Complete: | |

MATH 110A- 110B | Optimization I and Optimization II |

MATH 130B | Probability II |

B. Complete five electives from the list below, with at least one course outside of MATH. Other options may be chosen in consultation with the Data Science concentration advisor | |

Mathematical Modeling | |

Dynamical Systems | |

The Theory of Differential Equations | |

Introduction to Abstract Algebra: Rings and Fields | |

Stochastic Processes | |

Fixed Income | |

Mathematics of Financial Derivatives | |

Analysis in Several Variables | |

Complex Analysis | |

Introduction to Differential Geometry I | |

Introduction to Differential Geometry II | |

Introduction to Cryptology I | |

Introduction to Cryptology II | |

Combinatorics | |

Mathematics of Finance | |

Mathematical Machine Learning | |

Statistical Methods for Data Analysis I | |

Statistical Methods for Data Analysis II | |

Introduction to Artificial Intelligence | |

Neural Networks and Deep Learning | |

Applications of Probability in Computer Science | |

Machine Learning and Data-Mining | |

Algorithms for Probabilistic and Deterministic Graphical Models | |

Introduction to Computational Biology | |

Artificial Intelligence in Biology and Medicine | |

Computational Systems Biology |

##### Sample Program — Applied and Computational Mathematics Major Concentrating in Data Science

Freshman | ||
---|---|---|

Fall | Winter | Spring |

MATH 2A | MATH 2B | MATH 3A |

STATS 7 | PHYSICS 7C | MATH 9 |

General Education/Elective | General Education/Elective | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

Sophomore | ||

Fall | Winter | Spring |

MATH 2D | MATH 2E | MATH 3D |

MATH 13 | MATH 10 | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

Junior | ||

Fall | Winter | Spring |

MATH 105A- 105LA | MATH 105B- 105LB | MATH 121B |

MATH 130A | MATH 121A | Upper-Division Math Elective |

General Education/Elective | MATH 130B | Upper-Division Math Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

Senior | ||

Fall | Winter | Spring |

MATH 140A | MATH 110A | MATH 110B |

Non-Math Elective | MATH 140B | Upper-Division Math Elective |

General Education/Elective | Upper-Division Math Elective | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

#### Requirements for Applied and Computational Mathematics Major with a Concentration in Mathematical Finance

Admission to this concentration requires approval in advance by the Mathematical Finance advisor. Students need a GPA of 3.0 in lower-division and upper-division mathematics courses to be admitted to the concentration. The department may limit the number of students admitted into this concentration during impacted years. The admissions process begins with completing a form and submitting it to the Mathematical Finance advisor, followed by an interview. This approval should be applied for after the student has completed ECON 20A-ECON 20B, but no later than the end of the junior year.

Core requirements for all Mathematics majors plus: | |

Lower-Division Requirements: | |

A. Complete: | |

MATH 10 | Introduction to Programming for Data Science |

STATS 7 | Basic Statistics |

PHYSICS 7C | Classical Physics |

ECON 20A- 20B | Basic Economics I and Basic Economics II |

Upper-Division Requirements: | |

A. Complete the following upper-division MATH courses: | |

MATH 130B | Probability II |

MATH 130C | Stochastic Processes |

MATH 134A | Fixed Income |

MATH 134B | Mathematics of Financial Derivatives |

MATH 134C | Mathematical Models for Finance |

MATH 176 | Mathematics of Finance |

B. Complete the following six required upper-division ECON courses: | |

ECON 105A- 105B- 105C | Intermediate Quantitative Economics I and Intermediate Quantitative Economics II and Intermediate Quantitative Economics III |

ECON 122A | Applied Econometrics I |

or ECON 123A | Econometrics I |

ECON 132A | Introduction to Financial Investments |

ECON 134A | Corporate Finance |

or ECON 161A | Money and Banking |

##### Sample Program - Applied and Computational Mathematics Major Concentrating in Mathematical Finance

Freshman | ||
---|---|---|

Fall | Winter | Spring |

MATH 2A | MATH 2B | MATH 2D |

STATS 7 | MATH 9 | MATH 10 |

General Education/Elective | General Education/Elective | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

Sophomore | ||

Fall | Winter | Spring |

MATH 2E | MATH 3A | MATH 3D |

ECON 20A | ECON 20B | MATH 13 |

PHYSICS 7C | General Education/Elective | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

Junior | ||

Fall | Winter | Spring |

MATH 130A | MATH 130B | MATH 130C |

MATH 121A | MATH 121B | MATH 134A |

ECON 105A | ECON 105B | ECON 105C |

General Education/Elective | General Education/Elective | General Education/Elective |

Senior | ||

Fall | Winter | Spring |

MATH 105A- 105LA | MATH 105B- 105LB | MATH 134C |

ECON 134A | MATH 140A | MATH 140B |

ECON 132A | MATH 134B | ECON 122A |

General Education/Elective | MATH 176 | General Education/Elective |

#### Requirements for Applied and Computational Mathematics Major with a Specialization in Mathematical Biology

Core requirements for all Mathematics majors plus: | |

Lower-Division Requirements: | |

A. Complete: | |

BIO SCI 93- 93L | From DNA to Organisms and DNA to Organisms - Introduction to Biology Research |

BIO SCI 94- 94L | From Organisms to Ecosystems and Organisms to Ecosystems - Introduction to Biology Research Analysis |

MATH 10 | Introduction to Programming for Data Science |

Upper-Division Requirements: | |

A. Complete the following upper-division MATH courses: | |

MATH 112A- 112B | Introduction to Partial Differential Equations and Applications I and Introduction to Partial Differential Equations and Applications II |

MATH 113A- 113B | Mathematical Modeling in Biology I and Mathematical Modeling in Biology II |

MATH 115 | Mathematical Modeling |

B. Complete three elective courses, at least two MATH courses numbered 100-189. The third elective may be either a MATH course numbered 100-189 or a 4-unit upper-division Biological Sciences courses with advanced approval by the Mathematical Biology advisor. |

##### Sample Program - Applied and Computational Mathematics Major Specializing in Mathematical Biology

Freshman | ||
---|---|---|

Fall | Winter | Spring |

MATH 2A | MATH 2B | MATH 2D |

BIO SCI 93- 93L | BIO SCI 94- 94L | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

Sophomore | ||

Fall | Winter | Spring |

MATH 2E | MATH 3A | MATH 3D |

MATH 9 | MATH 10 | MATH 13 |

General Education/Elective | General Education/Elective | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

Junior | ||

Fall | Winter | Spring |

MATH 113A | MATH 113B | MATH 115 |

MATH 105A- 105LA | MATH 105B- 105LB | MATH 130A |

General Education/Elective | General Education/Elective | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

Senior | ||

Fall | Winter | Spring |

MATH 112A | MATH 112B | MATH 140B |

MATH 121A | MATH 121B | Upper-Division Math Elective |

Upper-Division Bio Sci Elective | MATH 140A | General Education/Elective |

General Education/Elective | Upper-Division Math Elective | General Education/Elective |

The Honors Program in Applied and Computational Mathematics is designed for students contemplating graduate work in applied mathematics. The program is open to junior and senior Mathematics majors who meet the minimum academic qualifications of a 3.5 GPA in Mathematics courses and a 3.2 GPA overall. It is highly recommended that students meet with the Honors Advisor by the beginning of their junior year to begin planning courses. Students should officially apply for the Honors Program no later than the fall quarter of their senior year. Recognition for completing the program is conferred upon graduation.

Participants must meet the following requirements:

A. Complete the requirements for the major in Applied and Computational Mathematics (in any one of its tracks) | |

B. Complete: | |

MATH 130B- 130C | Probability II and Stochastic Processes |

C. Complete one of the following series: | |

MATH H140A | Honors Introduction to Graduate Analysis I |

MATH H140B | Honors Introduction to Graduate Analysis II |

MATH H140C | Honors Introduction to Graduate Analysis III |

or | |

MATH 140C and MATH 134A-MATH 134B | |

or | |

MATH 140C and MATH 112A-MATH 112B | |

or | |

MATH 140C and MATH 113A-MATH 113B | |

or | |

MATH 140C and MATH 117-MATH 118 | |

or | |

MATH 140C and MATH 110A-MATH 110B | |

D. Complete one quarter of MATH 199 or a research project and thesis approved by the Honors Program Advisor. |

These requirements are in addition to the Applied and Computational Mathematics major requirements and the requirements for any specialization/concentration. MATH H140A-MATH H140B-MATH H140C may be used to satisfy upper-division electives or taken in place of MATH 140A-MATH 140B-MATH 140C and MATH 141.

NOTE: If all requirements are completed and the student's work and final GPA satisfies the program restrictions, the student will graduate with Honors in Mathematics, and this distinction is noted on the transcript.

##### Sample Program - Applied and Computational Mathematics Major Honors Program

Freshman | ||
---|---|---|

Fall | Winter | Spring |

MATH 2A | MATH 2B | MATH 2D |

STATS 7 | PHYSICS 7C | MATH 13 |

General Education/Elective | General Education/Elective | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

Sophomore | ||

Fall | Winter | Spring |

MATH 2E | MATH 3D | MATH 10 |

MATH 3A | MATH 9 | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

Junior | ||

Fall | Winter | Spring |

MATH 105A- 105LA | MATH 105B- 105LB | MATH 130C |

MATH 130A | MATH 130B | MATH 121B |

Upper-Division Math Elective | MATH 121A | Non-Math Elective |

General Education/Elective | General Education/Elective | General Education/Elective |

Senior | ||

Fall | Winter | Spring |

MATH H140A | MATH H140B | MATH H140C |

MATH 112A | MATH 112B | MATH 115 |

MATH 199 | Upper-Division Math Elective | Upper-Division Math Elective |

Non-Math Elective | General Education/Elective | General Education/Elective |

In order to prepare for independent study/independent research, it is highly recommended that students take at least one course sequence in the field they are interested in studying. The following list contains the major mathematical disciplines and the course work suggested for completion prior to doing independent study in that field:

For all Mathematics majors, or prospective majors, assistance in planning a program of study is available from the School of Physical Sciences academic counselors, as well as from the Mathematics Department Undergraduate Advisor for the various tracks. The application process for the specializations and concentrations requires students to plan a program of study with the assistance of a faculty advisor (https://www.math.uci.edu/undergraduate-studies/concentrations-and-specializations).