AST 392D -- Robinson

AST 392D Mathematical Techniques in Astronomy

Course Description and Syllabus, Spring 1998

UNIQUE NUMBER: 43175

INSTRUCTOR: Edward L. Robinson
Office: RLM 17.318
Telephone: 471-3401

LECTURE TIME: TTh 2:00-3:00 p.m.

LECTURE LOCATION: RLM 15.216B

REQUIRED TEXTBOOK: Date Reduction and Error Analysis for the Physical Sciences, by Bevington and Robinson

COURSE DESCRIPTION: The purpose of this course is to teach the mathematical methods needed by observers to reduce and analyze astronomical data, and by theoreticians to fully understand observations results. The syllabus of the course is heavily conditioned by utility: At the end of the course students will be able to calculate typical astronomical applications of

probability and statistics (e.g., error analysis)
least squares fits (e.g., fit a function to data)
time-series analysis (e.g., signal detection and echo mapping)
image analysis (e.g., noise filtering and image reconstruction)
The class grade will be based on regular homeworks and in-class mid-term and final exams.

Course Syllabus

1.	Probability and Statistics	(4 weeks)
	basic laws of probability
	Bayesian statistics (briefly!)
	probability distributions: binomial, Poisson, Gaussian, and c²
	moments of distributions: mean values and standard deviations
	correlation and covariance; the covariance matrix
	propagation of errors
	sampling theory: weighted means and standard deviations

2.	Least Squares	(3 weeks)
	maximum likelihood and least squares techniques
	linear least squares
	weighted least squares
	non-linear least squares; optimization methods.

3.	Fourier Analysis	(3 weeks)
	finite and infinite Fourier series
	Fourier transforms
	the power spectrum
	practical matters: windows, aliasing, noise

4.	Univariate Spectral Analysis	(2 weeks)
	convolution and the convolution theorem
	autocovariance and autocorrelation functions
	moving average processes and autoregressive processes
	digital filtering
	relation to Fourier transforms

5.	Bivariate Spectral Analysis	(0.5 week)
	cross correlation functions
	bivariate and moving average processes

6.	Maximum Entropy Analysis	(1.5 week)
	maximum entropy principle
	applications: MEM spectral analysis and image reconstruction

UNIQUE NUMBER:	43175
INSTRUCTOR:	Edward L. Robinson Office: RLM 17.318 Telephone: 471-3401
LECTURE TIME:	TTh 2:00-3:00 p.m.
LECTURE LOCATION:	RLM 15.216B
REQUIRED TEXTBOOK:	Date Reduction and Error Analysis for the Physical Sciences, by Bevington and Robinson
COURSE DESCRIPTION:	The purpose of this course is to teach the mathematical methods needed by observers to reduce and analyze astronomical data, and by theoreticians to fully understand observations results. The syllabus of the course is heavily conditioned by utility: At the end of the course students will be able to calculate typical astronomical applications of probability and statistics (e.g., error analysis) least squares fits (e.g., fit a function to data) time-series analysis (e.g., signal detection and echo mapping) image analysis (e.g., noise filtering and image reconstruction) The class grade will be based on regular homeworks and in-class mid-term and final exams.