# Course Information

Currently, 37 credit hours of coursework (including at least four graduate seminars) in courses numbered 5000 or above are required for completion of a Ph.D. (We do not currently offer an M.S. program). Students who began prior to Fall 2015 must take 39 credit hours, and those who started in Fall 2015 must take 38.

In their first two years, students take the five 3-credit core courses, plus some number of 1-credit seminars and other (2 or 3 credit) electives. Nominally, at least 4 APS-department seminars (i.e., ASTR 6000 or ASTR 5835) must be taken over a student's time in the program. The core courses are offered every year, and seminars are offered every semester. Some elective courses are offered once every two years.

Many of these courses encourage working with peers to approach problems from different angles. Click here to see how this requirement works with the CU honor code.

Below, we provide lists of pre-approved courses for possible inclusion in the 37-credit requirement. If you would like to take a course that does not appear in the lists given below and have it count toward your 37-credit requirement, please submit a request to the Associate Chair for Graduate Studies (currently S. Cranmer) for approval.

## APS Core

**Atomic and Molecular Processes (****ASTR 5110****)**

Thermal, mechanical, quantum, and radiative processes in gases and plasmas, with emphasis on spectroscopy, atomic and molecular physics, statistical mechanics, and kinetic theory, with applications in astrophysics, planetary physics, and plasmas.

**Radiative and Dynamical Processes (****ASTR 5120****)**

An introduction to radiative and dynamical processes aimed at graduate students in astrophysics, space physics and planetary science. Covers transport phenomena, the macroscopic treatment of radiation fields, magnetohydrodynamics and dynamical processes associated with planetary orbits and N-body systems.

**Introduction to Fluid Dynamics (****ASTR 5400****)**

Covers equations of fluid motion relevant to planetary atmospheres and oceans, as well as stellar atmospheres; effects of rotation and viscosity; and vorticity dynamics, boundary layers, and wave motions. Introduces instability theory, nonlinear equilibration, and computational methods in fluid dynamics.

See the standard syllabus. (Cross-listed as ATOC 5400 and PHYS 5400.)

**Mathematical Methods (****ASTR 5540****)**

Applied mathematics course designed to provide the necessary analytical and numerical background for courses in astrophysics, plasma physics, fluid dynamics, electromagnetism, and radiation transfer. Subjects covered include integration techniques, linear and nonlinear differential equations, WKB and Fourier transform methods, adiabatic invariants, partial differential equations, integral equations, and integrodifferential equations.

See the standard syllabus. (Cross-listed as ATOC-5540.)

**Observations, Data Analysis, and Statistics (****ASTR 5550****)**

Introduces multi-wavelength observational techniques, their limitations, and effects of various noise sources. Describes basic data handling, error analysis, and statistical tests relevant to modeling. Topics include probability distributions, model-fitting algorithms, confidence intervals, correlations, sampling, and convolution. Students derive physical measurements and uncertainties with hands-on analysis of real datasets.

**APS Electives**

- ASTR 5140: Astrophysical and Space Plasmas (cross-listed: PHYS 5141)
- ASTR 5300: Introduction to Magnetospheres
- ASTR 5330: Cosmochemistry (cross-listed: GEOL 5330)
- ASTR 5410: Fluid Instabilities, Waves, and Turbulence
- ASTR 5700: Stellar Astrophysics
- ASTR 5710: High-Energy Astrophysics
- ASTR 5720: Galaxies
- ASTR 5760: Astrophysical Instrumentation
- ASTR 5770: Cosmology
- ASTR 5780: Mission Design and Development for Space Sciences (cross-listed: ASEN 5440)
- ASTR 5800: Planetary Surfaces and Interiors (planetary core, cross-listed: GEOL 5800)
- ASTR 5810: Planetary Atmospheres (planetary core, cross-listed: ATOC 5810, GEOL 5810)
- ASTR 5820: Origin and Evolution of Planetary Systems (planetary core, cross-listed: ATOC 5820, GEOL 5820)
- ASTR 5830: Topics in Planetary Science (planetary core, cross-listed: ATOC 5830, GEOL 5830, repeatable)
- ASTR 7500: Special Topics in Astrophysical and Planetary Sciences (repeatable)

**Seminars:**

- ASTR 5835: Seminar in Planetary Science (cross-listed: ATOC 5835, GEOL 5835, repeatable)
- ASTR 6000: Seminar in Astrophysics (repeatable)

**Not currently offered:**

- ASTR 5250: Planetary Aeronomy
- ASTR 5730: Stellar Atmospheres and Radiative Transfer
- ASTR 5740: Interstellar Astrophysics
- ASTR 5750: Observational Astronomy
- ASTR 7150: Magnetohydrodynamics

**Electives in Other Departments**

- APPM 5460: Methods in Applied Mathematics: Dynamical Systems and Differential Equations
- APPM 5560: Markov Processes, Queues, and Monte Carlo Simulat
- APPM 5720: Open Topics in Applied Mathematics: Data-Driven Modeling
- APPM 6610: Introduction to Numerical Partial Differential Equations
- ASEN 5050: Space Flight Dynamics
- ASEN 5210: Remote Sensing Seminar (1 credit)
- ASEN 5335: Aerospace Environment
- ASEN 5519: Special Topics
- ASEN 6008: Interplanetary Mission Design
- ASEN 6050: Space Instrumentation (cross-listed: ASTR 6050, GEOL 6050)
- ASEN 6060: Advanced Astrodynamics
- ASEN 6070: Satellite Geodesy
- ASEN 6337: Remote Sensing Data Analysis
- ATOC 5050: Atmospheric Thermodynamics and Dynamics
- ATOC 5151: Atmospheric Chemistry
- ATOC 5235: Introduction to Atmospheric Radiative Transfer and Remote Sensing (cross-listed: ASEN 5235)
- ATOC 5560: Radiative Processes in Planetary Atmospheres (cross-listed: ASTR 5560)
- ATOC 5815: Scientific Programming, Data Analysis, and Visualization Laboratory
- ATOC 5850: Numerical Methods Laboratory
- ATOC 6100: Modeling Weather and Climate
- ATOC 6800: Scientific Writing
- CSCI 5622: Machine Learning
- CSCI 5922: Neural Networks and Deep Learning
- CSCI 6118: Software Engineering for Scientists
- ECEN 5134: Electromagnetic Radiation and Antennas
- ECEN 5156: Physical Optics
- ECEN 5264: Electromagnetic Absorption, Scattering, and Propagation
- ECEN 5616: Optoelectric System Design
- ECEN 5634: Microwave and RF Laboratory
- GEOL 5093: Remote Sensing of the Environment
- GEOL 5150: Planetary Field Geology (2-credit field trip, repeatable)
- GEOL 5910: Geothermodynamics
- GEOL 6610: Earth and Planetary Physics 1 (cross-listed: ASTR 6610)
- GEOL 6620: Earth and Planetary Physics 2 (cross-listed: ASTR 6620)
- GEOL 6630: Earth and Planetary Physics 3 (cross-listed: ASTR 6630)
- GEOL 6650: Seminar in Geophysics (1 credit, cross-listed: ASTR 6650)
- JRNL 5812: Science Writing
- PHYS 5070: Introduction to Computational Physics
- PHYS 5150: Introductory Plasma Physics (cross-listed: ASTR 5150)
- PHYS 5210: Theoretical Mechanics
- PHYS 5250: Introduction to Quantum Mechanics 1
- PHYS 5260: Introduction to Quantum Mechanics 2
- PHYS 5460: Teaching and Learning Physics
- PHYS 5770: Gravitational Theory (Theory of General Relativity)
- PHYS 7160: Intermediate Plasma Physics (cross-listed: ASTR 7160)
- PHYS 7230: Statistical Mechanics
- PHYS 7240: Advanced Statistical Mechanics
- PHYS 7270: Introduction to Quantum Mechanics 3
- PHYS 7310: Electromagnetic Theory 1
- PHYS 7320: Electromagnetic Theory 2
- PHYS 7440: Theory of the Solid State
- PHYS 7570: Quantum Information and Computing
- PHYS 7810: Special Topics in Physics (repeatable)
- PHYS 7820: Topics in Scientific Writing
- PHYS 7830: Plasma Seminar (1 credit)
STAT 5100: Markov Processes, Queues, and Monte Carlo Simulations

STAT 5400: Advanced Statistical Modeling

- STAT 5610: Statistical Learning