The multidisciplinary minor in Scientific Computing is a natural complement to the curriculum for majors in the natural and physical sciences, mathematics, and computer science. Focused study in the area of scientific computation enriches learning in any of these disciplines, adding an applied emphasis and stressing the cross-fertilization of research methods across disciplines.
The advancement of science in many fields is becoming less discipline-specific, and nowhere is this more apparent than in the common tools used for challenging computational problems. For instance, the modeling, visualization and simulation of large-scale nonlinear systems are common to many fields of science and applied mathematics. A multidisciplinary minor in scientific computation provides students with a valuable, intellectually challenging experience and marketable skills applicable in many fields. The minor will help to stimulate collaboration and exchange among faculty in the sciences. The three departments responsible for staffing the minor are computer science, mathematics, and physics. This minor may be extended to include chemistry and/or biology in the future.
(From the 2011-13 Catalog)
A. Required Core
This course teaches introductory programming within a problem solving framework applicable to the sciences. The course emphasizes technical programming, introductory data storage techniques, and the processing of scientific data. There is an emphasis on designing and writing correct code using an easy to learn scientific programming language such as Python. Advanced excel spreadsheet concepts will be taught and utilized during the programming process.
Prerequisite: mathematics competency.
A course designed to provide undergraduates students with the basic computational tools and techniques needed for their study in science and mathematics. Students learn by doing projects that solve problems in physical sciences and mathematics using symbolic and compiled languages with visualization. By use of the Sage problem-solving environment and the Python programming language, the students learn programming and numerical analysis in parallel with scientific problem solving. Also offered as M356 and P356.
Prerequisites: CS106, M251, M252, and ST232.
This course is required for all Scientific Computing minors. Its purpose is to provide students the opportunity to develop a research project or participate in an ongoing research project under direction of a faculty advisor. The project must combine scientific computing tools and techniques with a substantive scientific or engineering problem. It is also intended to give students experience in experimental design, recordkeeping, and scientific writing. Also offered as M456 and P456.
Prerequisites: consent of both the faculty advisor and the minor supervisor, and CS/M/P 356.
This course serves physics majors as well as those mathematics majors whose area of interest is analysis. Topics include: Fourier series, the complex numbers, analytic functions, and derivatives and integrals of complex functions. Other topics may include Laurent series and residues, partial differential equations and boundary value problems. Prerequisites: M251 and M252.
Mathematical Methods for Science
This course serves physics majors as well as those mathematics majors whose area of interest is analysis. Topics include: Fourier series, complex numbers, analytic functions, and derivatives and integrals of complex functions. Other topics may include Laurent series and residues, partial differential equations, and boundary value problems. Offered in alternate spring semesters. Prerequisites: M251 and M252.
B. Two of the following courses:
This course is an analytical study of Newtonian mechanics, including the harmonic oscillator, central force motion, non-linear oscillators, and an introduction to the Lagrangian formulation.
Offered in alternate spring semesters. Prerequisites: M152 and P201/202.
This course is an introduction to the physics of electricity and magnetism at the intermediate undergraduate level. It examines the experimental evidence that led to the development of the theories of electromagnetism (electrostatics, polarization and dielectrics, magnetostatics and magnetization, electrodynamics, electromagnetic waves, potentials and fields, and radiation) and the development of Maxwell's laws. The mathematical analysis of electromagnetic situations uses vector calculus to a great degree, so students also are exposed to working with a variety of vector operators.
Offered in alternate spring semesters. Prerequisites: M251 and P211/212.
The course covers the PIC18F4520 and Arduino microcontrollers as a paradigmatic microprocessor; other devices may be used as well. A brief survey of number systems, logic gates and Boolean algebra are followed by a study of the structure of microprocessors and the architecture of microprocessor systems. Programming microprocessors and the use of an assembler and a higher-level language (C) is covered. Peripheral interface devices are studied along with some wired logic circuits. Students gain experience through the use of microprocessor simulators and hardware implementations.
Offered in alternate spring semesters. Prerequisites: CS106 and P314.
This course expands on the ideas of quantum mechanics introduced in P304, and develops the necessary formalisms and tools for further work. Topics include the Schrödinger equation in its time-independent and time-dependent forms, an introduction to operators, square-well and harmonic oscillator potentials, scattering, the hydrogen atom, angular momentum, and perturbation theory.
Offered in alternate fall semesters. Prerequisites: M252 and P304.
Robyn Wangberg, Ph.D., Supervisor
Saint Mary's University of Minnesota
700 Terrace Heights #32
Winona, MN 55987-1399
(800) 635-5987, Ext. 1580