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Twin Cities Campus

Physics Minor

School of Physics & Astronomy
College of Liberal Arts
  • Program Type: Undergraduate minor related to major
  • Requirements for this program are current for Spring 2017
  • Required credits in this minor: 37
See the major description for more information.
Program Delivery
This program is available:
  • via classroom (the majority of instruction is face-to-face)
Minor Requirements
Physics minors must take all required physics and mathematics courses A-F (except those offered S-N only). Students may earn no more than one degree in the Department of Physics: a BA or a BS or a minor.
Mathematics
Take 12 credits.
MATH 1371 - CSE Calculus I [MATH] (4.0 cr)
or MATH 1271 - Calculus I [MATH] (4.0 cr)
MATH 1372 - CSE Calculus II (4.0 cr)
or MATH 1272 - Calculus II (4.0 cr)
MATH 2373 - CSE Linear Algebra and Differential Equations (4.0 cr)
or MATH 2243 - Linear Algebra and Differential Equations (4.0 cr)
or Honors Sequence
MATH 1571H - Honors Calculus I [MATH] (4.0 cr)
MATH 1572H - Honors Calculus II (4.0 cr)
MATH 2573H - Honors Calculus III (4.0 cr)
Physics Sequence
Take 25 credits.
PHYS 2201 - Introductory Thermodynamics and Statistical Physics (4.0 cr)
Physics I
PHYS 1301W - Introductory Physics for Science and Engineering I [PHYS, WI] (4.0 cr)
or PHYS 1401V - Honors Physics I [PHYS, WI] (4.0 cr)
or PHYS 1501V {Inactive} [PHYS, WI] (4.0 cr)
Physics II
PHYS 1302W - Introductory Physics for Science and Engineering II [PHYS, WI] (4.0 cr)
or PHYS 1402V - Honors Physics II [PHYS, WI] (4.0 cr)
or PHYS 1502V {Inactive} [PHYS, WI] (4.0 cr)
Physics III
PHYS 2503 - Physics III: Intro to Waves, Optics, and Special Relativity (4.0 cr)
or PHYS 2503H - Honors Physics III (4.0 cr)
Quantum Physics
PHYS 2601 - Quantum Physics (4.0 cr)
PHYS 2605 {Inactive} (3.0 cr)
Physics/Astrophysics Elective
Take 3 or more credit(s) from the following:
· PHYS 3022 - Introduction to Cosmology (3.0 cr)
· PHYS 4001 - Analytical Mechanics (4.0 cr)
· PHYS 4002 - Electricity and Magnetism (4.0 cr)
· PHYS 4041 - Computational Methods in the Physical Sciences (4.0 cr)
· PHYS 4051 - Methods of Experimental Physics I (5.0 cr)
· PHYS 4052W - Methods of Experimental Physics II [WI] (5.0 cr)
· PHYS 4101 - Quantum Mechanics (4.0 cr)
· PHYS 4121W - History of 20th-Century Physics [WI] (3.0 cr)
· PHYS 4201 - Statistical and Thermal Physics (3.0 cr)
· PHYS 4211 - Introduction to Solid-State Physics (3.0 cr)
· PHYS 4303 - Electrodynamics and Waves (3.0 cr)
· PHYS 4511 - Introduction to Nuclear and Particle Physics (3.0 cr)
· PHYS 4611 - Introduction to Space Physics (3.0 cr)
· PHYS 4621 - Introduction to Plasma Physics (3.0 cr)
· PHYS 4911 - Introduction to Biopolymer Physics (3.0 cr)
· PHYS 5001 - Quantum Mechanics I (4.0 cr)
· PHYS 5002 - Quantum Mechanics II (4.0 cr)
· PHYS 5011 - Classical Physics I (4.0 cr)
· PHYS 5012 - Classical Physics II (4.0 cr)
· PHYS 5022 - Relativity, Cosmology, and the Universe (4.0 cr)
· PHYS 5041 - Mathematical Methods for Physics (4.0 cr)
· PHYS 5042 {Inactive} (4.0 cr)
· PHYS 5081 - Introduction to Biopolymer Physics (3.0 cr)
· PHYS 5201 - Thermal and Statistical Physics (3.0 cr)
· PHYS 5401 {Inactive} (4.0 cr)
· PHYS 5402 {Inactive} (4.0 cr)
· PHYS 5621 - Introduction to Plasma Physics (3.0 cr)
· PHYS 5701 - Solid-State Physics for Engineers and Scientists (4.0 cr)
· AST 4002 - Astrophysics II (4.0 cr)
· AST 4001 - Astrophysics I (4.0 cr)
· AST 4031 - Interpretation and Analysis of Astrophysical Data (4.0 cr)
· AST 4041 - Computational Methods in the Physical Sciences (4.0 cr)
· AST 5001 {Inactive} (4.0 cr)
· AST 5012 - The Interstellar Medium (4.0 cr)
· AST 5022 - Relativity, Cosmology, and the Universe (4.0 cr)
· AST 5201 - Methods of Experimental Astrophysics (4.0 cr)
 
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· College of Liberal Arts
View future requirement(s):
· Fall 2022
· Fall 2020
· Fall 2018


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· Physics Minor
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MATH 1371 - CSE Calculus I (MATH)
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 1271/Math 1281/Math 1371/
Typically offered: Every Fall & Spring
Differentiation of single-variable functions, basics of integration of single-variable functions. Applications: max-min, related rates, area, curve-sketching. Use of calculator, cooperative learning. prereq: CSE or pre-bioprod concurrent registration is required (or allowed) in biosys engn (PRE), background in [precalculus, geometry, visualization of functions/graphs], instr consent; familiarity with graphing calculators recommended
MATH 1271 - Calculus I (MATH)
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 1271/Math 1281/Math 1371/
Typically offered: Every Fall, Spring & Summer
Differential calculus of functions of a single variable, including polynomial, rational, exponential, and trig functions. Applications, including optimization and related rates problems. Single variable integral calculus, using anti-derivatives and simple substitution. Applications may include area, volume, work problems. prereq: 4 yrs high school math including trig or satisfactory score on placement test or grade of at least C- in [1151 or 1155]
MATH 1372 - CSE Calculus II
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 1272/Math 1282/Math 1372/
Typically offered: Every Spring
Techniques of integration. Calculus involving transcendental functions, polar coordinates, Taylor polynomials, vectors/curves in space, cylindrical/spherical coordinates. Use of calculators, cooperative learning. prereq: Grade of at least C- in [1371 or equiv], CSE or pre-Bioprod/Biosys Engr
MATH 1272 - Calculus II
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 1272/Math 1282/Math 1372/
Typically offered: Every Fall, Spring & Summer
Techniques of integration. Calculus involving transcendental functions, polar coordinates. Taylor polynomials, vectors/curves in space, cylindrical/spherical coordinates. prereq: [1271 or equiv] with grade of at least C-
MATH 2373 - CSE Linear Algebra and Differential Equations
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2243/Math 2373/Math 2574H
Typically offered: Every Fall & Spring
Linear algebra: basis, dimension, eigenvalues/eigenvectors. Differential equations: linear equations/systems, phase space, forcing/resonance, qualitative/numerical analysis of nonlinear systems, Laplace transforms. Use of computer technology. prereq: [1272 or 1282 or 1372 or 1572] w/grade of at least C-, CSE or pre-Bio Prod/Biosys Engr
MATH 2243 - Linear Algebra and Differential Equations
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2243/Math 2373/Math 2574H
Typically offered: Every Fall, Spring & Summer
Linear algebra: basis, dimension, matrices, eigenvalues/eigenvectors. Differential equations: first-order linear, separable; second-order linear with constant coefficients; linear systems with constant coefficients. prereq: [1272 or 1282 or 1372 or 1572] w/grade of at least C-
MATH 1571H - Honors Calculus I (MATH)
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 1271/Math 1281/Math 1371/
Grading Basis: A-F only
Typically offered: Every Fall
Differential/integral calculus of functions of a single variable. Emphasizes hard problem-solving rather than theory. prereq: Honors student and permission of University Honors Program
MATH 1572H - Honors Calculus II
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 1272/Math 1282/Math 1372/
Grading Basis: A-F only
Typically offered: Every Fall & Spring
Continuation of 1571. Infinite series, differential calculus of several variables, introduction to linear algebra. prereq: 1571H (or equivalent) honors student
MATH 2573H - Honors Calculus III
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2263/Math 2374/Math 2573H
Grading Basis: A-F only
Typically offered: Every Fall
Integral calculus of several variables. Vector analysis, including theorems of Gauss, Green, Stokes. prereq: Math 1572H (or equivalent), honors student
PHYS 2201 - Introductory Thermodynamics and Statistical Physics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Thermodynamics and its underlying statistical nature. Prereq: PHYS 1302W or equivalent
PHYS 1301W - Introductory Physics for Science and Engineering I (PHYS, WI)
Credits: 4.0 [max 4.0]
Course Equivalencies: Phys 1201W/1301W/1401V/1501V
Typically offered: Every Fall, Spring & Summer
Use of fundamental principles to solve quantitative problems. Motion, forces, conservation principles, structure of matter. Applications to mechanical systems. Prereq or Concurrent: MATH 1271/1371/1371H or equivalent
PHYS 1401V - Honors Physics I (PHYS, WI)
Credits: 4.0 [max 4.0]
Course Equivalencies: Phys 1201W/1301W/1401V/1501V
Grading Basis: A-F only
Typically offered: Every Fall
Comprehensive, calculus-level general physics. Emphasizes use of fundamental principles to solve quantitative problems. Description of motion, forces, conservation principles. Structure of matter, with applications to mechanical systems. Prereq: Honors program or with permission, Prereq or Concurrent: MATH 1271/1371/1571H or equivalent
PHYS 1302W - Introductory Physics for Science and Engineering II (PHYS, WI)
Credits: 4.0 [max 4.0]
Course Equivalencies: Phys 1202W/1302W/1402V/1502V
Typically offered: Every Fall & Spring
Use of fundamental principles to solve quantitative problems. Motion, forces, conservation principles, fields, structure of matter. Applications to electromagnetic phenomena. Prereq: PHYS 1301 or equivalent, Prereq or Concurrent: MATH 1272/1372/1572H or equivalent
PHYS 1402V - Honors Physics II (PHYS, WI)
Credits: 4.0 [max 4.0]
Course Equivalencies: Phys 1202W/1302W/1402V/1502V
Grading Basis: A-F only
Typically offered: Every Spring
Fundamental principles to solve quantitative problems. Description of motion, forces, conservation principles, fields. Structure of matter, with applications to electro-magnetic phenomena. Honors program or with permission, PHYS 1401V or equivalent, Prereq or CC: MATH 1272/1372/1572H or equivalent
PHYS 2503 - Physics III: Intro to Waves, Optics, and Special Relativity
Credits: 4.0 [max 4.0]
Course Equivalencies: Phys 2303/2403H/2503/2503H
Typically offered: Every Fall
Third semester of introductory physics. Mechanical/electromagnetic waves, optics, special relativity. prereq: 1302W or equivalent
PHYS 2503H - Honors Physics III
Credits: 4.0 [max 4.0]
Course Equivalencies: Phys 2303/2403H/2503/2503H
Grading Basis: A-F only
Typically offered: Every Fall
The third semester of a calculus-based introductory physics sequence. Topics include: relativistic kinematics and dynamics, mechanical and electromagnetic waves, light, interference, diffraction, wave-particle duality, and topics in modern physics. Course emphasizes the use of fundamental problems to solve quantitative problems. Intended primarily for those who have completed 1401V/1402V, although those students with outstanding performance in 1301W/1302W may be granted permission to enroll. Prereq: Honors program or with permission, PHYS 1402V or equivalent
PHYS 2601 - Quantum Physics
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Introduction to quantum mechanics. Applications to atomic, molecular, condensed-matter, nuclear, elementary-particle, and statistical physics. Prereq: PHYS2503/2503H, Recommended Concurrent: Phys 3041
PHYS 3022 - Introduction to Cosmology
Credits: 3.0 [max 3.0]
Typically offered: Spring Odd Year
Large-scale structure and history of universe. Dark matter, cosmic microwave background. Newtonian/relativistic world models. Physics of early universe. Cosmological tests. Prereq: PHYS 2601
PHYS 4001 - Analytical Mechanics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Analytic Newtonian mechanics. Mathematics beyond prerequisites developed as required. Prereq: PHYS 2503/2503H or equivalent, PHYS 3041
PHYS 4002 - Electricity and Magnetism
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Classical theory of electromagnetic fields using vector algebra and vector calculus. prereq: PHYS 3041, PHYS 2503/2503H or equivalent
PHYS 4041 - Computational Methods in the Physical Sciences
Credits: 4.0 [max 4.0]
Course Equivalencies: Ast 4041/Phys 4041
Typically offered: Periodic Fall & Spring
Introduction to using computer programs to solve problems in physical sciences. Selected numerical methods, mapping problems onto computational algorithms. Arranged lab. Prereq: PHYS 3041
PHYS 4051 - Methods of Experimental Physics I
Credits: 5.0 [max 5.0]
Typically offered: Every Fall
Contemporary experimental techniques. Introduction to modern analog and digital electronics from an experimental viewpoint. Use of computers for data acquisition and experimental control. Statistics of data analysis. Prereq or Concurrent PHYS 3605W, PHYS 3041
PHYS 4052W - Methods of Experimental Physics II (WI)
Credits: 5.0 [max 5.0]
Typically offered: Every Spring
Second semester of laboratory sequence. Contemporary experimental techniques illustrated by experiments with data analysis. Students design and execute an experimental project. Lectures on specialized topics of professional concern. prereq: PHYS 4051
PHYS 4101 - Quantum Mechanics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Mathematical techniques of quantum mechanics. Schrodinger Equation and simple applications. General structure of wave mechanics. Operator methods, perturbation theory, radiation from atoms. Prereq: PHYS 3041, PHYS 2601
PHYS 4121W - History of 20th-Century Physics (WI)
Credits: 3.0 [max 3.0]
Course Equivalencies: HSci 4121/Phys 4121
Grading Basis: OPT No Aud
Typically offered: Periodic Spring
The transition from classical to modern physics (relativity, quantum) and its architects (from Planck and Einstein to Heisenberg and Schrödinger). The WWII bomb projects in the US and in Germany. Post-war developments (solid state, particle physics). Prereq: calculus or permission from the instructor.
PHYS 4201 - Statistical and Thermal Physics
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Principles of thermodynamics and statistical mechanics. Selected applications such as kinetic theory, transport theory, and phase transitions. Prereq: PHYS 3041, PHYS 2201, PHYS 2601
PHYS 4211 - Introduction to Solid-State Physics
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
A modern presentation of the properties of solids. Topics include vibrational and electronic properties of solids; diffraction of waves in solids and electron band structure. Other possible topics include optical properties, magnetic phenomena, and superconductivity. prereq: 2201, 4101
PHYS 4303 - Electrodynamics and Waves
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Analytical mechanics. Electricity/magnetism, including mechanical/electromagnetic wave phenomena. Physical/geometrical optics. Prereq: PHYS 4002
PHYS 4511 - Introduction to Nuclear and Particle Physics
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Fundamental particles and Standard Model. Symmetries/quarks, models of nuclei, interactions between particles/nuclei, tests of conservation laws, fission/fusion. prereq: 4101
PHYS 4611 - Introduction to Space Physics
Credits: 3.0 [max 3.0]
Typically offered: Fall Odd Year
Dynamics of charged particles/plasmas in space. Physics of the Sun and solar wind. Solar/galactic cosmic rays. Interactions of solar wind with planetary magnetospheres. Dynamics of Magnetosphere. Formation of the aurora. Physics of radiation belts. prereq: PHYS 4001, PHYS 4002
PHYS 4621 - Introduction to Plasma Physics
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall & Spring
Basic properties of collisionless, magnetized plasmas, single particle motion, plasmas as fluids, magnetohydrodynamics, waves in plasmas, equilibrium, instabilities, kinetic theory/shocks. Prereq: PHYS 4001, PHYS 4002
PHYS 4911 - Introduction to Biopolymer Physics
Credits: 3.0 [max 3.0]
Course Equivalencies: Phys 4911/5081
Typically offered: Every Spring
Introduction to biological and soft condensed matter physics. Emphasizes physical ideas necessary to understand behavior of macromolecules and other biological materials. Elements of thermodynamics and statistical mechanics are presented as needed. Prereq: PHYS 2201 or equivalent
PHYS 5001 - Quantum Mechanics I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Schrodinger equation: bound state and scattering problems in one dimension. Spherically symmetric problems in three dimensions, angular momentum, and the hydrogen atom. Approximation methods for stationary states. Time-dependent perturbation theory. Operators and state vectors: general formalism of quantum theory. prereq: 4101 or equiv or instr consent
PHYS 5002 - Quantum Mechanics II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Symmetry in quantum mechanics, space-time symmetries and the rotation group, Clebsch-Gordan coefficients and the Wigner-Eckart theorem. Scattering theory. Method of second quantization with elementary applications. Relativistic wave equations including Dirac equation. prereq: 5001 or equiv
PHYS 5011 - Classical Physics I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Classical mechanics: Lagrangian/Hamiltonian mechanics, orbital dynamics, rigid body motion, special relativity. prereq: 4001, 4002 or instr consent
PHYS 5012 - Classical Physics II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Classical electromagnetism: electrostatics, magnetostatics, Maxwell's equations, electromagnetic waves, radiation, interaction of charged particles with matter. prereq: 5011 or instr consent
PHYS 5022 - Relativity, Cosmology, and the Universe
Credits: 4.0 [max 4.0]
Course Equivalencies: Ast 5022/Phys 5022
Typically offered: Periodic Fall
Large-scale structure and history of universe. Introduction to Newtonian and relativistic world models. Physics of early universe. Cosmological tests. Formation of galaxies. prereq: 2601 or instr consent
PHYS 5041 - Mathematical Methods for Physics
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Survey of mathematical techniques needed in analysis of physical problems. Emphasizes analytical methods. prereq: 2601 or grad student
PHYS 5081 - Introduction to Biopolymer Physics
Credits: 3.0 [max 3.0]
Course Equivalencies: Phys 4911/5081
Typically offered: Every Spring
Introduction to biological and soft condensed matter physics. Emphasizes physical ideas necessary to understand behavior of macromolecules and other biological materials. prereq: PHYS 2201 or equivalent
PHYS 5201 - Thermal and Statistical Physics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Equilibrium Statistical Mechanics. General Principles of Statistical Mechanics: Ensembles. Derivation of Thermodynamics from statistical principles. Classical Systems. Quantum Statistical Mechanics: Fundamentals. Photons. Ideal Fermi & Bose Gases. Non-ideal gases. Introduction to Phase Transitions. prereq: [[4101, 4201] or equiv] previous exposure to thermodynamics, introductory statistical physics
PHYS 5621 - Introduction to Plasma Physics
Credits: 3.0 [max 3.0]
Course Equivalencies: Phys 4621/Phys 5621
Typically offered: Periodic Fall
Basic properties of collisionless, magnetized plasmas, single particle motion, plasmas as fluids, magnetohydrodynamics, waves in plasmas, equilibrium, instabilities, kinetic theory/shocks. prereq: CSE grad student, working knowledge of waves/electromagnetism
PHYS 5701 - Solid-State Physics for Engineers and Scientists
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall & Spring
Crystal structure and binding; diffraction; phonons; thermal and dielectric properties of insulators; free electron model; band structure; semiconductors. prereq: Grad or advanced undergrad in physics or engineering or the sciences
AST 4002 - Astrophysics II
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Astrophysics of galaxies and the universe. Diffuse matter, galactic structure, and evolution. Clusters of galaxies. Introductory cosmology, evolution of the universe. prereq: 2001, Phys 2601
AST 4001 - Astrophysics I
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Astrophysics of stars and stellar populations. Stellar formation, evolution, interiors/atmospheres. Stellar populations, galactic distribution of stars. prereq: 2001, Phys 2601
AST 4031 - Interpretation and Analysis of Astrophysical Data
Credits: 4.0 [max 4.0]
Grading Basis: A-F only
Typically offered: Every Spring
Introduction to analysis techniques with applications to modern astrophysics. Methods to interpret/analyze large data sets from experiments. Principles/methods of analysis, with applications to current research. For senior undergraduate/graduate students in Physics/Astronomy. prereq: [Math 2243 or 2373 or equivalent[, [Math 2263 or 2374 or equivalent], Ast 2001 or instr consent
AST 4041 - Computational Methods in the Physical Sciences
Credits: 4.0 [max 4.0]
Course Equivalencies: Ast 4041/Phys 4041
Typically offered: Periodic Fall & Spring
Introduction to using computer programs to solve problems in physical sciences. Selected numerical methods, mapping problems onto computational algorithms. Arranged lab. Prereq: PHYS 3041
AST 5012 - The Interstellar Medium
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall & Spring
Survey of physical processes in the interstellar medium. Dynamic processes, excitation processes, emission and absorption by gas and dust. Hot bubbles, HII regions, molecular clouds. prereq: 2001, Phys 2601 or instr consent
AST 5022 - Relativity, Cosmology, and the Universe
Credits: 4.0 [max 4.0]
Course Equivalencies: Ast 5022/Phys 5022
Typically offered: Periodic Fall & Spring
Large-scale structure/history of universe. Introduction to Newtonian/relativistic world models. Physics of early universe, cosmological tests, formation of galaxies. prereq: [2001, Phys 2601] or instr consent
AST 5201 - Methods of Experimental Astrophysics
Credits: 4.0 [max 4.0]
Typically offered: Spring Even Year
Contemporary astronomical techniques and instrumentation. Emphasizes data reduction and analysis, including image processing. Students make astronomical observations at O'Brien Observatory and use department's computing facilities for data analysis. Image processing packages include IRAF, AIPS, IDL, MIRA. prereq: Upper div CSE or grad or instr consent