Option 2 packages

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The Option 2 math major requires six math courses and four courses in an area of application. These four courses are required to have a certain mathematical content. They should also form a coherent collection of courses that reflect a plan to study some discipline outside of mathematics that uses a fair amount of mathematics. The selection of the four courses, together with the six required math courses must be approved by the student's advisor. This page lists some sample packages in several popular areas.

Economics and Business

Actuarial Mathematics

Actuaries use techniques in mathematics and statistics to evaluate risk in a variety of areas including insurance, finance, healthcare, and even criminal justice. In recent history the field has been revolutionized by advances in the theory of probability and the ability to access, store, and process very large data sets.

Professional actuaries are currently in great demand, have lucrative pay, and is a growth field [1]. Similar to some other fields (law, accounting, etc.) there are professional organizations which administer a series of examinations [2]. Oftentimes students complete some of these examinations before graduating which allows them to move right into a career (Note: these exams are not required for graduation).

Students who are interested in actuarial mathematics should consider coursework in probability, statistics, analysis, as well as computational mathematics.

Application Courses

  • Act. Sci 650 and 652
  • Act. Sci. 651 or 653

Core Math Courses

  • Probability: Math 309 or Math 431 or 531
    • Math 431 is preferred over 309.
    • Math 531 is advanced probability and may be taken only after Math 421 or Math 521.
  • Statistics: Math 310
    • Has the prerequisite: one of the probability courses mentioned above AND an elementary stats class (Stat 302 is recommended).

Additional Courses to Consider

Also: Students interested in the areas of mathematics with applications to actuarial science might consider the following as well:

  • Consider combining the major with a program offered by the UW-Madison School of Business.

Business

Applications of mathematics to business is often referred to as Operations Research or Management Science. Specifically, the goal is to use mathematics to make the best decisions in a variety of areas: searching, routing, scheduling, transport, etc.

The modern version of the field grew out of the work mathematicians did in order to aid the Allied war effort during world war II.[3] Since then, the field has grown into a robust and active area of research and scholarship including several journals and professional organizations.[4]

Students interested in applications of mathematics to business can find many employment opportunities in private corporations, government agencies, nonprofit enterprises, and more. Students can also move onto postgraduate programs in mathematics or business.

Application Courses

  • Linear programming and Optimization: Math 525
  • Operations Research: OTM 410
  • At least two from the following: Gen Bus 304; OTM 451, 411, 633, 654
    • Note that OTM 633 is crosslisted with math. It cannot be used as both an application course AND a core math course.

Core Math Courses

  • Linear Algebra
  • Probability: Math 309 or Math 431 or 531
    • Math 431 is preferred over 309.
    • Math 531 is advanced probability and may be taken only after Math 421 or Math 521.

Additional Courses to Consider

  • Additional courses in computational mathematics.
  • Math 633.

Also: Consider combining this program with a program in the UW-Madison School of Business.

Economics

Finance

Physical Sciences

The physical sciences and mathematics have grown hand-in-hand since antiquity. Students with strong backgrounds in mathematics who are also interested in a branch of the physical sciences can find opportunities in laboratories, engineering firms, education, finance, law, business, and medicine. Those with very strong academic records can find themselves as preferred candidates for graduate study in their choice of field.

The following sample programs in mathematics have strong relationships with a particular area of interest in the natural sciences.

Atmospheric & Oceanic Sciences

Weather and climate is determined by the interaction between two thin layers which cover the planet: The oceans and the atmosphere. Understanding how these two fluids act and interact allow humans to describe historical climate trends, forecast near future weather with incredible accuracy, and hopefully describe long term climate change which will affect the future of human society.

A student interested in atmospheric and oceanic studies who has a strong mathematics background can find a career working in local, national, and international meteorological laboratories. These include private scientific consulting businesses as well as public enterprises. Students interested in graduate study could find their future studies supported by the National Science Foundation, the Department of Energy, NASA, or others [5]. There is a large amount of funding available in the area due to the relevance research findings have on energy and economic policy.

Mathematicians who work in Atmospheric and oceanic studies are drawn to the complexities of the problems and the variety of methods in both pure and applied mathematics which can be brought to bear on them. Students should take coursework in methods of applied mathematics, differential equations, computational mathematics, and differential geometry and topology.

Application Courses

  • Physics 208 or Physics 248 [6]
    • Both of these classes have prerequisites (Physics 207/247).
  • ATM OCN 310, 311, and 330 [7]
    • 310 and 330 have Physics 208/248 as a prerequisite.

Core Mathematics Courses

Additional Courses to Consider

  • Dynamical Systems: Math 415
  • Probability: Math 309 or Math 431 or 531
    • Math 431 is preferred over 309.
    • Math 531 is advanced probability and may be taken only after Math 421 or Math 521.
  • Computational Mathematics: 513 or 514
  • Analysis: Math 521
  • Differential Geometry: Math 561
  • Partial Differential Equations: Math 619

Also: Students who are interested in this area might consider

Chemistry

The applications of mathematics to chemistry range from the mundane: Ratios for chemical reactants; to the esoteric: Computational methods in quantum chemistry. Research in this latter topic lead to a Nobel Prize in Chemistry to John Pople[8] who was a mathematician.

All areas of pure and applied mathematics have applications in modern chemistry. The most accessible track features coursework focusing on applied analysis and computational math. Students with a strong interest in theoretical mathematics should also consider modern algebra (for group theory) and topology.

Application Courses

  • Physics 208 or Physics 248 [9]
    • Both of these classes have prerequisites (Physics 207/247).
  • Analytical Chemistry: Chem 327 or Chem 329[10]
    • Prerequisite: Chem 104 or 109
  • Physical Chemistry: Chem 561 and 562

Core Math Courses

Additional Courses to Consider

  • Dynamical Systems: Math 415
  • Several higher level courses have connections to theoretical chemistry: Modern Algebra (Math 541), Topology (Math 551), Differential Geometry (Math 561), and Complex Analysis (Math 623)
    • Any of these courses are acceptable in lieu of the 500 level courses above.

Also: Consider combining this program with one offered by the Department of Chemistry.

Physics and Astronomy

Perhaps the subject with the strongest historical ties with mathematics is physics. Certainly some of the great physical theories have been based on novel applications of mathematical theory or the invention of new subjects in the field: Newtonian mechanics and calculus, relativity and Riemannian geometry, quantum theory and functional analysis, etc.

Nearly all mathematics courses offered here at UW Madison will have some applications to physics. The following is a collection of courses which would support general interest in physics.

Application Courses

  • Mechanics, Electricity, and Magnetism: Physics 311 and Physics 322
  • Physics Electives: At least two 3-credit physics courses above the 400 level. These cannot include labs. Suggested courses are Physics 415, 448, 449, 525, 531, 535, 545, and 551.

Core Mathematics Courses

Additional Courses to Consider

  • Dynamical Systems: Math 415
  • Probability: Math 309 or Math 431 or 531
    • Math 431 is preferred over 309.
    • Math 531 is advanced probability and may be taken only after Math 421 or Math 521.
  • Additional courses above the 500 level.

Also: Consider combining this program with one offered by the Department of Physics or Department of Astronomy.

Biological Sciences

Applications of mathematics to biology has undergone a recent boom. Historically, the biologist was perhaps most interested in applications of calculus, but now nearly any modern area of mathematical research has an application to some biological field[11]. The following lists some possibilities.

Bio-Informatics

Bioinformatics is the application of computational methods to understand biological information. Of course the most interesting items of biological information is genetic and genomic information. Considering that the human genome has over three billion basepairs [12], it's no wonder that many mathematicians find compelling problems in the area to devote their time.

Students with strong mathematical backgrounds who are interested in bioinformatics can find careers as a part of research teams in public and private laboratories across the world [13]. Moreover, many universities have established interdisciplinary graduate programs promoting this intersection of mathematics, biology, and computer science [14].

Students interested in bioinformatics should have a strong background in computational mathematics and probability. Students should also have a strong programming background.

Application Courses

  • Computer Science: CS 302 and CS 367
  • Bioinformatics: BMI/CS 576
  • Genetics: Gen 466
    • Note that this class has a prerequisite of a year of chemistry and a year of biology coursework. Please contact the UW-Madison genetics program for more information.

Core Mathematics Courses

  • Linear Algebra
    • Students who use either Math 320 or Math 340 to fulfill their Linear Algebra requirement must take Math 421 before any mathematics course numbered above 500.
  • Probability: Math 309 or Math 431 or 531
    • Math 431 is preferred over 309.
    • Math 531 is advanced probability and may be taken only after Math 421 or Math 521.

Additional Courses to Consider

Also

  • Students might consider combining this program with one in Computer Science or Genetics.
  • Complete this major with a few additional courses if you are interested in medical school [15].

Bio-Statistics

Biostatistics is the application of mathematical statistical methods to areas of biology. Historically, one could consider the field to have been founded by Gregor Mendel himself. He used basic principles of statistics and probability to offer a theory for which genetic traits would arise from cross hybridization of plants and animals. His work was forgotten for nearly fifty years before it was rediscovered and become an integral part of modern genetic theory.

Beyond applications to genetics, applications of biostatistics range from public health policy to evaluating laboratory experimental results to tracking population dynamics in the field. Currently, health organizations consider there to be a shortage of trained biostatisticians[16]. Students interested in this area should find excellent job prospects.

Students interested in biostatistics should have strong backgrounds in probability, statistics, and computational methods.

Application Courses

  • Statistics: Stat 333, 424, and 575 [17]
    • Stat 333 has as a prerequisite some experience with statistical software. This can be achieved by also registering for Stat 327. Stat 327 is a single credit course which does not count for the mathematics major
  • Biostatistics: at least one of Stat 641 or 642

Core Mathematics Courses

  • Linear Algebra
    • Students who use either Math 320 or Math 340 to fulfill their Linear Algebra requirement must take Math 421 before any mathematics course numbered above 500.
  • Probability: Math 309 or Math 431 or 531
    • Math 431 is preferred over 309.
    • Math 531 is advanced probability and may be taken only after Math 421 or Math 521.

Additional Courses to Consider

  • More courses in computational mathematics listed above.
  • Math 635

Also

Ecology

Forestry

Genetics

Structural Biology

Structural biologists are primarily interested in the large molecules which are involved in cellular processes. As such, these molecules are the fundamental chemical building blocks of life. The field lies on the intersection of biology, physics, chemistry, and mathematics and so structural biology is an exciting area of interdisciplinary research.

In general, the mathematics involved in structural biology is focused on computational methods, probability, and statistics. Note that we offer a specialized course in Mathematics Methods in Structural Biology - Math 606.

Application Courses

  • Analytical Methods in Chemistry: Chem 327 or 329
  • Physical Chemistry: Chem 561 and 562
  • Mathematical Methods in Structural Biology: Math 606

Core Math Courses

Additional Courses to Consider

Also: Consider combining the program with one in Biology, Biochemistry, or Chemistry.

Systems Biology

Systems biology is the computational and mathematical modeling of biological systems at any scale. The classical example of this may be the predator-prey model of differential equations which describe the relative population dynamics of two species. Other systems examples include disease transmission, chemical pathways, cellular processes, and more.

In general, the mathematics involved in structural biology is focused on computational methods, dynamical systems, differential equations, the mathematics of networks, control theory, and others. Note that we offer a specialized course in Mathematical Methods in Systems Biology - Math 609.

Application Courses

  • Organic Chemistry: Chem 341 or 343
  • Introductory Biochemistry: Biochem 501
  • Mathematical Methods in Structural Biology: Math 609
  • One Biochem elective: Any Biochem class numbered above 600. Suggested courses are Biochem 601, 612, 620, 621, 624, and 630.

Core Math Courses

Additional Courses to Consider

  • Probability: Math 309 or Math 431 or 531
    • Math 431 is preferred over 309.
    • Math 531 is advanced probability and may be taken only after Math 421 or Math 521.
  • Additional courses in computational mathematics: 513, 514, Math 515, Math 525

Also: Consider combining the program with one in Biology, Biochemistry, or Chemistry.

Engineering

Chemical Engineering

The following program details an option 2 package for students in the College of Engineering program in Chemical Engineering who are interested in pursuing a second major in mathematics.

Application Courses

  • CBE 320, 326, 426, 470
    • Note: All of these course are required for the undergraduate program in chemical engineering.
    • Several of these courses have as a prerequisite other engineering and science courses.

Core Math Courses

Additional Courses to Consider

  • Additional courses above the 500 level listed above.
  • Probability: Math 309 or Math 431 or 531
    • Math 431 is preferred over 309.
    • Math 531 is advanced probability and may be taken only after Math 421 or Math 521.
  • Stochastic Processes: Math 632

Civil Engineering

The following program details an option 2 package for students in the College of Engineering program in Civil and Environmental Engineering who are interested in pursuing a second major in mathematics.

Application Courses

  • Core Fluid Mechanics and Structural Analysis: CIV ENG 310, 311, 340
    • Note: All of these course are required for the undergraduate program in civil engineering.
    • Several of these courses have as a prerequisite other engineering and science courses.
  • One elective Structural Analysis Course: CIV ENG 440, 442, 445, or 447.
    • Each of these courses may be used as an elective in the undergraduate program in civil engineering.

Core Math Courses

Additional Courses to Consider

  • Dynamical Systems: Math 415
  • Additional courses above the 500 level listed above.
  • Probability: Math 309 or Math 431 or 531
    • Math 431 is preferred over 309.
    • Math 531 is advanced probability and may be taken only after Math 421 or Math 521.

Electrical and Computer Engineering

The following program details an option 2 package for students in the College of Engineering program in Computer and Electrical Engineering who are interested in pursuing a second major in mathematics.

Application Courses

  • Core ECE: ECE 220, 230, 352
    • Note: All of these course are required for the undergraduate program in electrical and computer engineering.
    • Several of these courses have as a prerequisite other engineering and science courses.
  • One elective: ECE 435, 525, or 533.
    • Each of these courses may be used as an elective in the undergraduate program in civil engineering.
    • ECE 435 is crosslisted with math. It cannot be used as both an application course AND a core math course.

Core Math Courses

Additional Courses to Consider

  • Additional courses above the 500 level listed above.
  • Probability: Math 309 or Math 431 or 531
    • Math 431 is preferred over 309.
    • Math 531 is advanced probability and may be taken only after Math 421 or Math 521.
  • Stochastic Processes: Math 632
  • Error correcting codes: Math 641

Engineering Mechanics and Astronautics

The following program details an option 2 package for students in the College of Engineering program in Engineering Mechanics and Astronautics who are interested in pursuing a second major in mathematics.

Application Courses

  • Core Engineering Mechanics: EMA 201, 202, 303
  • One elective: EMA 521, 542, 545, or 563
    • All of the above courses may be used to satisfy the EMA program requirements.

Core Math Courses

Additional Courses to Consider

  • Dynamical Systems: Math 415
  • Additional courses above the 500 level listed above.


Industrial Engineering

Materials Science

The following program details an option 2 package for students in the College of Engineering program in Materials Science and Engineering who are interested in pursuing a second major in mathematics.

Application Courses

  • Core Materials Courses: MSE 330, 331, and 351
  • One Engineering Elective: CBE 255, CS 302, CS 310, ECE 230, ECE 376, EMA 303, Phys 321, Stat 424].
    • All of the above classes may be used to satisfy the program requirements for MS&E BS degree.

Core Math Courses

Additional Courses to Consider

  • Dynamical Systems: Math 415
  • Additional courses above the 500 level listed above.

Mechanical Engineering

The following program details an option 2 package for students in the College of Engineering program in Mechanical Engineering who are interested in pursuing a second major in mathematics.

Application Courses

  • Core Mechanical Engineering Courses: ME 340, 361, 363, 364
    • All of the above courses are required by the Mechanical Engineering program.

Core Math Courses

Additional Courses to Consider

  • Dynamical Systems: Math 415
  • Additional courses above the 500 level listed above.

Nuclear Engineering

The following program details an option 2 package for students in the College of Engineering program in Nuclear Engineering who are interested in pursuing a second major in mathematics.

Application Courses

  • Core Nuclear Engineering Courses: NE 305, 405, and 408
  • One Engineering Elective: Physics 321 or 322, ECE 376, BME 501, or NE 411.
    • All of the above classes may be used to satisfy the program requirements for the Nuclear Engineering BS degree.

Core Math Courses

Additional Courses to Consider

  • Dynamical Systems: Math 415.
  • Probability: Math 309 or Math 431 or 531
    • Math 431 is preferred over 309.
    • Math 531 is advanced probability and may be taken only after Math 421 or Math 521.
  • Stochastic Processes: Math 632.
  • Additional courses above the 500 level listed above.

Computer Science

Cryptography

Theoretical Computer Science

Education

Statistics

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