Homework over the last two years is now several thousand pages, and I need to organize some of the information I return to regularly. These are titles which have more specific purpose than general reference. General texts are for subjects new to me. I have in each case selected a single book to use as a self-study course.
The literature on signals is all Coming Up. Oppenheim's signal systems text can be completed without first learning DiffEQ, but I am not in a rush to get to signal processing. Attending the audio panel at Pax Dev, none of the problems described required signal processing to fix.
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Click on any title to see related posts
Blogger doesn't get organization. Suggestions welcome!
100 Great Problems of Elementary Mathematics: Their History and Solutions
Heinrich Dörrie
Had this book for a while; Last month I decided to work through all 100 problems in depth, from the beginning.
{Amazon page}
Elements
Euclid
The 13 books of the Elements can be done very quickly, and I am still deciding how to use them. After completing book I in a day, I realized I wanted a greater understanding. I'd like to work out all the algebra and vector transforms introduced by each new Proposition. The resulting numerical methods would be a geometer's toolsbox for navigating 3-space. Less efficient than the worst CAD environment, surely; but I believe well worth the practice. I wished to use the blog to help me organize the information, and work out clean, presentable transforms, but typing math into Blogger is a misery.
{Google Ebook}
Disquisitiones Arithmeticae
Carl Friedrich Gauss
{Available as a free Google Ebook}
Theory and Application of Infinite Series
Konrad Knopp
{Amazon Page}
A First Course in Numerical Analysis
Anthony Ralston and Philip Rabinowitz
{Amazon page}
Matrices and Linear Algebra
Hans Schneider and George Philip Barker
(Completed 2010) Checked every theorem and proof; done all problems except the last chapter.
{Amazon page}
Advanced Calculus
David Widder
I use this book as regular reference. Completed the sections on partial differentiation, vectors, differential geometry, and the Stieltjes integral. I know it inside and out; again, I do every problem except where they were repetitive or I failed to find a solution.
Widder is a giant poo and assumes you will do the problem sets by rote, ignorant of the gaping assumptions until he brings them to your attention. The problem sets are poorly arranged.
On the other hand, he is terrifically concise.
2011-
Théorie analytique de la chaleur
Joseph Fourier
{Free Google ebook}
Applied Vector Analysis
Hwei P. Hsu
Plowing through this book right now (Mar '12). Much is review; I am focused on
-working with geometric primitives directly in vector notation
-solving problems in different notations: algebra, geometry, linear combinations of vectors, vector-valued functions
-clearing up any confusions about the core methods.
-acquiring surface and line integrals
-completing the book as quickly as possible
Principia
Isaac Newton
{Available in a number of editions for free. I have a print copy, but do not recommend the edition}
Ordinary Differential Equations: An ElementaryTextbook for Students of Mathematics, Engineering and the Sciences
Morris Tenenbaum and Harry Pollard
Status: Halfway; up to Simple Harmonic Motion. I alternated between this book and Linear Algebra for about a year. Linear Equations of Order Greater Than One occupied the first half of 2011 before I took a break. I do every problem, except where they are repetitive and I no longer need the practice.
Feynman Lectures on Computation
Richard P. Feynman
Read it and tried many of the exercises, but I was not yet familiar enough with the territory. I will revisit it soon.
{Amazon Page}
Introduction to Algorithms
Thomas Cormen, Charles Leiserson, Ronald Rivest.
1st Edition
{Amazon page}
The Measurement of Power Spectra
R. B. Blackmann and J. W. Tukey
{Amazon page}
An Introduction to Harmonic Analysis
Yitzhak Katznelson
{Amazon page}
The Science of Radio
Paul J. Nahin
I'll have to substitute my own SciLab code for the Electronics Workbench and Matlab exercises. Which means I have to learn SciLab! Rad!
{Amazon page}
An Introduction to Random Vibrations, Spectral and Wavelet Analysis
D.E. Newland
(3rd edition) A civil and mechanical engineering text! Guaranteed not to treat spectral analysis as a subset of aesthetics.
{Amazon page}
Signals and Systems: An Introduction to Analog and Digital Signal Processing
Alan Oppenheim, Alan Wilsky, Ian Young
{My edition is old. It corresponds to the:}
MIT OpenCourseWare Online Course in Digital Signal Processing
The Fourier Transform and its Applications
Brad Osgood
Online video series with accompanying materials through Stanford University. (EE261)
Musimathics (2 vols.) Gareth Loy
Comprehensive reference for music-related mathematical systems, analysis, etc.
{Amazon Page}
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