The mathematics named option programs allow students to develop a deep understanding of how the subject relates to other areas of human inquiry. The requirements for these programs feature mathematics courses with topics inspired by and commonly applied to problems in these associated fields. Though often paired with a second major in a related area, these programs function well alone and are suited to any mathematics student with a variety of interests. Students interested in a named option program are recommended to meet with an advisor to navigate the various plans and courses available to them. Advising information can be found on the BA or BS pages.

The named options do not support honors in the major.

The Mathematics for the Physical and Biological Sciences program requires 10 distinct courses for at least 30 credits as described below. While a single courses may be used to fulfill more than one requirement, it will only contribute once to the total course count. Finally, only one course from each of the following groupings may be used to fulfill course and credit requirements: Intro Linear Algebra (MATH 320, MATH 340, MATH 341, MATH 375), Intro Differential Equations (MATH 319, MATH 320 or MATH 376), and Intro Probability (MATH/STAT 309 or MATH/STAT 431).

Code | Title | Credits |
---|---|---|

Core Math Requirement (minimum of six distinct MATH courses for at least 18 credits) ^{1} | ||

Linear Algebra | 3-5 | |

Linear Algebra and Differential Equations | ||

or MATH 340 | Elementary Matrix and Linear Algebra | |

or MATH 341 | Linear Algebra | |

or MATH 375 | Topics in Multi-Variable Calculus and Linear Algebra | |

Differential Equations | 0-5 | |

Techniques in Ordinary Differential Equations | ||

or MATH 320 | Linear Algebra and Differential Equations | |

or MATH 376 | Topics in Multi-Variable Calculus and Differential Equations | |

Intermediate Mathematics Requirement (complete at one) | 0-6 | |

Applied Mathematical Analysis and Applied Mathematical Analysis | ||

Topics in Multi-Variable Calculus and Linear Algebra | ||

Linear Algebra | ||

The Theory of Single Variable Calculus | ||

Advanced Mathematics Requirement (complete one) | 3 | |

Numerical Analysis | ||

Ordinary Differential Equations | ||

Analysis I | ||

Probability Theory | ||

Linear Algebra II | ||

Modern Algebra | ||

Elementary Topology | ||

Differential Geometry | ||

Analysis of Partial Differential Equations | ||

Complex Analysis | ||

MATH Elective to reach six courses and 18 credits | 3-9 | |

At least one from: ^{1} | ||

Numerical Linear Algebra | ||

Numerical Analysis | ||

Ordinary Differential Equations | ||

Analysis I | ||

Analysis II | ||

Linear Optimization | ||

Probability Theory | ||

Mathematical Methods in Data Science | ||

Linear Algebra II | ||

Modern Algebra | ||

Modern Algebra | ||

Elementary Topology | ||

Elementary Geometric and Algebraic Topology | ||

Differential Geometry | ||

Modern Number Theory | ||

Fundamentals of Set Theory | ||

Mathematical Logic | ||

Stochastic Methods for Biology | ||

Mathematical Methods for Systems Biology | ||

Analysis of Partial Differential Equations | ||

Complex Analysis | ||

Introduction to Fourier Analysis | ||

Introduction to Measure and Integration | ||

Introduction to Stochastic Processes | ||

An Introduction to Brownian Motion and Stochastic Calculus | ||

Remaining courses/credits may be from: | ||

Introduction to Probability and Mathematical Statistics II | ||

Applied Mathematical Analysis | ||

Applied Mathematical Analysis | ||

Applied Dynamical Systems, Chaos and Modeling | ||

The Theory of Single Variable Calculus | ||

Introduction to Combinatorial Optimization | ||

Introduction to the Theory of Probability | ||

Introduction to Probability and Mathematical Statistics I | ||

Applied Linear Algebra | ||

Introduction to Combinatorics | ||

Natural/Biological Sciences Requirement (Four courses distinct from the above for at least 12 credits) ^{1} | 12-16 | |

A Modern Introduction to Physics | ||

or PHYSICS 207 | General Physics | |

or PHYSICS 201 | General Physics | |

or E M A 201 | Statics | |

A Modern Introduction to Physics | ||

or PHYSICS 208 | General Physics | |

or PHYSICS 202 | General Physics | |

Two additional courses from the following: ^{2} | ||

Stellar Astrophysics | ||

The Interstellar Medium | ||

Dynamics of the Atmosphere and Ocean I | ||

Dynamics of the Atmosphere and Ocean II | ||

Science of Climate Change | ||

Physics of the Atmosphere and Ocean I | ||

Physics of the Atmosphere and Ocean II | ||

Cellular Biology | ||

Physical Chemistry | ||

or CHEM 565 | Biophysical Chemistry | |

Physical Chemistry | ||

Programming II | ||

Problem Solving Using Computers | ||

Data Programming II | ||

Programming III | ||

Introduction to Combinatorial Optimization | ||

Introduction to Combinatorics | ||

Numerical Linear Algebra | ||

Numerical Analysis | ||

Linear Optimization | ||

Introduction to Geophysics: The Dynamic Earth | ||

Practical Applications of GPS Surveying | ||

Quantitative Methods for Geoscience | ||

Introduction to Applied Geophysics | ||

Hydrogeology | ||

A Modern Introduction to Physics | ||

or PHYSICS 241 | Introduction to Modern Physics | |

or PHYSICS 205 | Modern Physics for Engineers | |

Mechanics | ||

Electric Circuits and Electronics | ||

Electromagnetic Fields | ||

Electromagnetic Fields | ||

Optics | ||

Scientific Background to Global Environmental Problems | ||

Radiological Physics and Dosimetry | ||

Introduction to Plasmas | ||

Solid State Physics | ||

Radionuclides in Medicine and Biology | ||

Electronic Aids to Measurement | ||

Applied Optics | ||

Introduction to Probability and Mathematical Statistics II | ||

or STAT 312 | Introduction to Theory and Methods of Mathematical Statistics II | |

Applied Regression Analysis | ||

Introduction to Time Series | ||

Introductory Nonparametric Statistics | ||

An Introduction to Sample Survey Theory and Methods | ||

Applied Categorical Data Analysis | ||

Statistical Experimental Design | ||

Introduction to the Theory of Probability | ||

Introduction to Probability and Mathematical Statistics I | ||

or STAT 311 | Introduction to Theory and Methods of Mathematical Statistics I | |

Applied Multivariate Analysis | ||

Financial Statistics | ||

Introduction to Computational Statistics | ||

Introduction to Combinatorics | ||

Linear Optimization | ||

Introduction to Stochastic Processes | ||

Computational Modeling of Biological Systems | ||

Mathematical Methods for Structural Biology | ||

Mathematical Methods for Systems Biology | ||

Plant Biochemistry | ||

Mechanisms of Enzyme Action | ||

Cellular Signal Transduction Mechanisms | ||

Engineering Principles for Biological Systems | ||

Quantitative Techniques for Biological Systems | ||

Structural Design for Agricultural Facilities | ||

Engineering Properties of Food and Biological Materials | ||

Measurements and Instrumentation for Biological Systems | ||

Rheology of Foods and Biomaterials | ||

Engineering Principles of Agricultural Machinery | ||

Bioinstrumentation | ||

Biomechanics | ||

Introductory Transport Phenomena | ||

Applied Statistics for Biomedical Engineers | ||

Engineering Principles of Molecules, Cells, and Tissues | ||

Radiological Physics and Dosimetry | ||

Biofluidics | ||

Stem Cell Bioengineering | ||

Medical Imaging Systems | ||

Introduction to Energy-Tissue Interactions | ||

Systems Biology: Mammalian Signaling Networks | ||

Biochemical Engineering | ||

Physics of Radiotherapy | ||

The Physics of Diagnostic Radiology | ||

Medical Image Science: Mathematical and Conceptual Foundations | ||

Tissue Mechanics | ||

Introduction to Chemical Process Modeling | ||

Chemical Process Thermodynamics | ||

Introductory Transport Phenomena | ||

Momentum and Heat Transfer Operations | ||

Engineering Principles of Molecules, Cells, and Tissues | ||

Fluid Mechanics | ||

Hydroscience | ||

Environmental Engineering Processes | ||

Structural Analysis I | ||

Transportation Engineering | ||

Uncertainty Analysis for Engineers | ||

Electrodynamics I | ||

Circuit Analysis | ||

Introduction to Solid State Electronics | ||

Electrodynamics II | ||

Signals and Systems | ||

Introduction to Cryptography | ||

Introduction to Error-Correcting Codes | ||

Dynamics | ||

or M E 240 | Dynamics | |

Mechanics of Materials | ||

or M E 306 | Mechanics of Materials | |

Practicum in Finite Elements | ||

Intermediate Problem Solving for Engineers | ||

Engineering Analysis I | ||

Engineering Analysis II | ||

Astrodynamics | ||

Simulation and Probabilistic Modeling | ||

Operations Research-Deterministic Modeling | ||

Uncertainty Analysis for Engineers | ||

Introduction to Decision Analysis | ||

Introduction to Optimization | ||

Linear Optimization | ||

Advanced Linear Programming | ||

Thermodynamics of Materials | ||

Transport Phenomena in Materials | ||

Macroprocessing of Materials | ||

Introduction to Thin-Film Deposition Processes | ||

Introduction to Computational Materials Science and Engineering | ||

Computer-Aided Engineering | ||

Dynamic Systems | ||

Introduction to Feedback Control for Mechanical Engineers | ||

Thermodynamics | ||

Statistical Experimental Design | ||

Fundamentals of Nuclear Engineering | ||

Introduction to Plasmas | ||

Methods for Probabilistic Risk Analysis of Nuclear Power Plants | ||

Radiological Physics and Dosimetry | ||

Medical Imaging Systems | ||

Introduction to Energy-Tissue Interactions | ||

Radionuclides in Medicine and Biology | ||

The Physics of Diagnostic Radiology | ||

Health Physics and Biological Effects | ||

Total Credits | 30 |

## Residency and quality of Work

- 2.000 GPA for all MATH courses and courses eligible for the major.
^{3} - 2.000 GPA on at least 15 credits of upper level credit in the major.
^{4} - 15 credits in MATH in the major taken on the UW-Madison campus.
^{5}

## Footnotes

^{1} | Courses listed in the tables below may have prerequisites outside of the program requirements. |

^{2} | Any MATH course from the elective list above may be used in lieu of any of the following courses. |

^{3} | This includes any course with the MATH prefix (or cross-listed with MATH) regardless of appearing in the tables above as well as only those non-MATH courses which appear in the tables above. |

^{4} | This includes any MATH courses (or courses cross-listed with MATH) numbered 307 and above, regardless of appearing in the tables above, as well as any non-MATH course listed in the tables above which carries the advanced LAS designation. |

^{5} | This includes any course with the MATH prefix (or cross-listed with MATH) numbered 307 and above. |

## Sample Four-Year Plan

This Sample Four-Year Plan is a tool to assist students and their advisor(s). Students should use it—along with their DARS report, the Degree Planner, and Course Search & Enroll tools—to make their own four-year plan based on their placement scores, credit for transferred courses and approved examinations, and individual interests. As students become involved in athletics, honors, research, student organizations, study abroad, volunteer experiences, and/or work, they might adjust the order of their courses to accommodate these experiences. Students will likely revise their own four-year plan several times during college.

In general, your four year plan in mathematics should be organized along the following sequence: 1) Calculus, 2) Linear Algebra, 3) Required Intermediate level course, 4) Additional intermediate level courses as needed, 5) Required advanced level course, 6) Additional advanced level courses.

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

Fall | Credits | Spring | Credits |

MATH 221 | 5 | MATH 222 | 4 |

Literature Breadth | 3 | Literature Breadth | 3 |

Communication A | 3 | Ethnic Studies | 3 |

Foreign Language ^{if required} | 4 | Foreign Language (if required) | 4 |

15 | 14 | ||

Sophomore | |||

Fall | Credits | Spring | Credits |

MATH 234^{1} | 4 | MATH 321 | 3 |

MATH 320 | 3 | Humanities Breadth | 3 |

Humanities Breadth | 3 | Elective | 6 |

Communication B | 3 | ||

Elective | 3 | ||

16 | 12 | ||

Junior | |||

Fall | Credits | Spring | Credits |

MATH 322 | 3 | Intermediate MATH elective | 3 |

PHYSICS 247, 207, 201, or E M A 201 | 5 | PHYSICS 248, 208, or 202 | 5 |

Social Sciences Breadth | 3 | Social Science Breadth | 3 |

Biological Sciences Breadth | 3 | Biological Sciences Breadth | 3 |

Elective | 3 | Elective | 3 |

17 | 17 | ||

Senior | |||

Fall | Credits | Spring | Credits |

Required Advanced MATH | 3 | Advanced MATH | 3 |

Natural/Biological requirement elective | 3 | Natural/Biological requirement elective | 3 |

Social Science Breadth | 3 | Social Science Breadth | 3 |

Elective | 6 | Elective | 5 |

15 | 14 | ||

Total Credits 120 |

## footnotes

^{1} | Students should declare their major upon the successful completion of this course |