Option 2 packages: Difference between revisions
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* Analysis: [http://www.math.wisc.edu/521-advanced-calculus Math 521] | * Analysis: [http://www.math.wisc.edu/521-advanced-calculus Math 521] | ||
* Stochastic Processes: [ | * Stochastic Processes: [http://www.math.wisc.edu/math-605stochastic-methods-biology Math 605] or [http://www.math.wisc.edu/632-introduction-stochastic-processes Math 632] | ||
* Computational Mathematics: At least one of [http://www.math.wisc.edu/443-applied-linear-algebra Math 443], [http://www.math.wisc.edu/513-numerical-linear-algebra 513], [http://www.math.wisc.edu/514-numerical-analysis 514], [http://www.math.wisc.edu/525-linear-programming-methods Math 525] | * Computational Mathematics: At least one of [http://www.math.wisc.edu/443-applied-linear-algebra Math 443], [http://www.math.wisc.edu/513-numerical-linear-algebra 513], [http://www.math.wisc.edu/514-numerical-analysis 514], [http://www.math.wisc.edu/525-linear-programming-methods Math 525] | ||
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'''Additional Courses to Consider''' | '''Additional Courses to Consider''' | ||
* More courses in computational mathematics listed above. | * More courses in computational mathematics listed above. | ||
* [ | * [http://www.math.wisc.edu/635-introduction-brownian-motion-and-stochastic-calculus Math 635] | ||
'''Also''' | '''Also''' | ||
* Consider combining this program with [ | * Consider combining this program with [http://www.stat.wisc.edu/undergrad/undergraduate-statistics-program Statistics] or a program in the [http://www.cals.wisc.edu/departments/major College of Agriculture and Life Sciences]. | ||
* Compare this major program to requirements for Medical School. | * Compare this major program to requirements for Medical School. | ||
Revision as of 22:29, 17 October 2014
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
- Linear Algebra: Math 320 or Math 340 or Math 341 or Math 375
- 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.
- Statistics: Math 310
- Has the prerequisite: one of the probability courses mentioned above AND an elementary stats class (Stat 302 is recommended).
- Analysis: Math 521
- Stochastic Processes: Math 632
- Linear Programming: Math 525
Additional Courses to Consider
- Combinatorics: Math 475
Also: Students interested in the areas of mathematics with applications to actuarial science might consider the following as well:
- Advanced courses offered by the Department of Statistics or even a dual major.
- Consider combining the major with a program offered by the UW-Madison School of Business.
Operations Research
Economics
Finance
Physical 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 [3]. 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 [4]
- Both of these classes have prerequisites (Physics 207/247).
- ATM OCN 310, 311, and 330 [5]
- 310 and 330 have Physics 208/248 as a prerequisite.
Core Mathematics Courses
- Linear Algebra: Math 340 or Math 341 or Math 375
- Differential Equations: Math 319
- Applied Analysis: Math 321 and 322
- Computational Mathematics: At least one of 513 or 514
- Theory of Differential Equations: Math 519
Additional Courses to Consider
- 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
- Combining the math major with the program offered by the Department of Atmospheric and Oceanic Sciences.
- The AMEP program.
Chemistry
Physics
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[6]. 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 [7], 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 [8]. Moreover, many universities have established interdisciplinary graduate programs promoting this intersection of mathematics, biology, and computer science [9].
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: Math 320 or Math 340 or Math 341 or Math 375
- 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.
- Combinatorics: Math 475
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 [10].
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.
Students interested in biostatistics should have strong backgrounds in probability, statistics, and computational methods.
Application Courses
- Statistics: Stat 333, 424, and 575 [11]
- 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: Math 320 or Math 340 or Math 341 or Math 375
- 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.
- Statistics: Math 310
- Analysis: Math 521
Additional Courses to Consider
- More courses in computational mathematics listed above.
- Math 635
Also
- Consider combining this program with Statistics or a program in the College of Agriculture and Life Sciences.
- Compare this major program to requirements for Medical School.