An Introduction to Error Analysis

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1. Al0neStarDec 2024
   These books are what i would consider the best books for self-study. (I have gone through many textbooks after i went back to school to study statistics.)

   • Real Analysis: A Long-Form Mathematics Textbook

   • Proofs: A Long-Form Mathematics Textbook

   • Mathematical Logic Through Python

   • A Course in Calculus and Real Analysis

   • A Course in Multivariable Calculus and Analysis

   • Differential Equations With Applications and Historical Notes

   • Probability and Random Processes (Grimmet)

   • Probability Through Problems

   • Fifty Challenging Problems in Probability with Solutions

   • The Simple and Infinite Joy of Mathematical Statistics

   • An Introduction to Error Analysis

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2. SteuardAug 2018
   I should probably write this up more formally somewhere. But have a look, and it would be cool if you'd give me credit somewhere if you use these notes in your own stuff (I'm Steuard Jensen, and I'm a professor at Alma College). For each course below, the books are listed in roughly my order of preference. This is far, far from being every book for each course or even every popular one, but it's a start.

   Intro Physics (Mechanics, E&M, waves, etc.):

   * Six Ideas That Shaped Physics, by Tom Moore: Conservation laws first, and a nice conceptual approach (and can incorporate "modern physics" along the way).

   * Matter and Interactions, by Chabay and Sherwood: Integrated VPython programming, and uses "true" relativistic mechanics right from the start (and quantum's built in, too).

   * Physics for Scientists and Engineers, by Randall Knight: As close to a "traditional" intro book as you can get while still paying attention to physics education research. It's very good, though I feel like the latest edition has veered back a bit to a bit more traditional order, perhaps to make it smoother for old professors to switch.

   Uncertanity/Error Analysis: (Essential for understanding experimental physics)

   * An Introduction to Error Analysis, by John Taylor: Such a beautiful little book!

   "Modern Physics": (Is a class whose content mostly ends before 1950 really "modern"?)

   * Six Ideas That Shaped Physics (Units R and Q), by Tom Moore: A very nice first introduction to both special relativity and quantum physics. Might need some supplemental content if you have time for more advanced quantum/nuclear stuff.

   [* Special Relativity, by Tom Helliwell: I learned out of this, and it was very good. I haven't taught out of it.]

   [* Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, by Eisberg and Resnick: I learned out of this, but haven't taught out of it. Comprehensive.]

   Intermediate Classical Dynamics: (I haven't taught this one!)

   * ?Classical Mechanics, by John Taylor: I've heard very good things about this one.

   [* Classical Dynamics of Particles and Systems, by Thornton and Marion: I learned out of it. It was fine.]

   Intermediate Electromagnetism:

   * Introduction to Electrodynamics, by David Griffiths: Truly excellent introduction to analysis of electric and magnetic fields using vector calculus and partial differential equations.

   [* ?Classical Electromagnetic Radiation, by Heald and Marion: I learned out of this. Not my favorite book, but it did the job.]

   Intermediate Quantum Mechanics:

   * A Modern Approach to Quantum Mechanics, by John Townsend: Inspired by Sakurai's graduate text, Townsend starts by studying spin and Stern-Gerlach experiments in depth using Dirac bra-ket notation, and then progresses to time evolution and position space. The chapter on the path integral formulation is fun but optional, and there's good stuff on perturbation theory and scattering and some hints toward field theory. (This may work best if students had a strong "Modern Physics" course first that studied wavefunctions in some depth.)

   [* Introduction to Quantum Mechanics, by David Griffiths: I haven't used this myself. An excellent quantum book with a more "traditional" organization, starting with wavefunctions and only later talking about Dirac notation and spin.]

   Thermodynamics and Statistical Mechanics:

   * An Introduction to Thermal Physics, by Daniel Schroeder: A fantastic, multi-pass blend of statistical mechanics and classical thermodynamics. It starts with basic classical definitions of thermal concepts, then introduces explicit state counting in medium-sized systems with the help of Excel, then discusses classical thermodynamics in depth, and finally goes into a full discussion Boltzmann factors and statmech.

   * Fundamentals of Statistical and Thermal Physics, by Frederick Reif: This was (for me) the least bad of the books that I used to teach myself undergraduate statmech while I was in graduate school. (I foolishly arranged to avoid the class as an undergrad.)

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3. geokonJul 2018
   A great starting book that helps build a good intution is "An Introduction to Error Analysis" by John Taylor (of Classical Mechanics fame). Basically if you are taking any kind of measurements and need to compose them intelligently this is where to start. From sig-figs to chi squared. A must read for any starting researcher

   My experience otherwise with stats books has been horrendous.. (havent found a good "medium level" book to move on to yet)

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4. geokonNov 2016
   Anyone have a recommendation on a good statistic textbook?

   Everything I've tried has been absolutely horrible except for "An Introduction to Error Analysis" by John Taylor (yeah the classical mechanics guy). Unfortunately it's a bit basic...

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