Tag: textbook

Basic Category Theory by Tom Leinster | Free Ebook Download

Basic Category Theory by Tom Leinster | Free Ebook Download
Basic Category Theory by Tom Leinster (arxiv.org)

This short introduction to category theory is for readers with relatively little mathematical background. At its heart is the concept of a universal property, important throughout mathematics. After a chapter introducing the basic definitions, separate chapters present three ways of expressing universal properties: via adjoint functors, representable functors, and limits. A final chapter ties the three together.
For each new categorical concept, a generous supply of examples is provided, taken from different parts of mathematics. At points where the leap in abstraction is particularly great (such as the Yoneda lemma), the reader will find careful and extensive explanations.

Tom Leinster has released a digital e-book copy of his textbook Basic Category Theory on arXiv.  [1]

h/t to John Carlos Baez for the notice:

My friend Tom Leinster has written a great introduction to that wonderful branch of math called category theory! It’s free:

https://arxiv.org/abs/1612.09375

It starts with the basics and it leads up to a trio of related concepts, which are all ways of talking about universal properties.

Huh? What’s a ‘universal property’?

In category theory, we try to describe things by saying what they do, not what they’re made of. The reason is that you can often make things out of different ingredients that still do the same thing! And then, even though they will not be strictly the same, they will be isomorphic: the same in what they do.

A universal property amounts to a precise description of what an object does.

Universal properties show up in three closely connected ways in category theory, and Tom’s book explains these in detail:

through representable functors (which are how you actually hand someone a universal property),

through limits (which are ways of building a new object out of a bunch of old ones),

through adjoint functors (which give ways to ‘freely’ build an object in one category starting from an object in another).

If you want to see this vague wordy mush here transformed into precise, crystalline beauty, read Tom’s book! It’s not easy to learn this stuff – but it’s good for your brain. It literally rewires your neurons.

Here’s what he wrote, over on the category theory mailing list:

…………………………………………………………………..

Dear all,

My introductory textbook “Basic Category Theory” was published by Cambridge University Press in 2014. By arrangement with them, it’s now also free online:

https://arxiv.org/abs/1612.09375

It’s also freely editable, under a Creative Commons licence. For instance, if you want to teach a class from it but some of the examples aren’t suitable, you can delete them or add your own. Or if you don’t like the notation (and when have two category theorists ever agreed on that?), you can easily change the Latex macros. Just go the arXiv, download, and edit to your heart’s content.

There are lots of good introductions to category theory out there. The particular features of this one are:
• It’s short.
• It doesn’t assume much.
• It sticks to the basics.

 

References

[1]
T. Leinster, Basic Category Theory, 1st ed. Cambridge University Press, 2014.

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Emily Riehl’s new category theory book has some good company

Emily Riehl’s new category theory book has some good company

Emily Riehl's new category theory book has some good company. It's a beautiful book by the way
Emily Riehl’s new category theory book has some good company. It’s a beautiful book by the way.

Instagram filter used: Clarendon

Photo taken at: UCLA Bookstore

I just saw Emily Riehl‘s new book Category Theory in Context on the shelves for the first time. It’s a lovely little volume beautifully made and wonderfully typeset. While she does host a free downloadable copy on her website, the book and the typesetting is just so pretty, I don’t know how one wouldn’t purchase the physical version.

I’ll also point out that this is one of the very first in Dover’s new series Aurora: Dover Modern Math Originals. Dover has one of the greatest reprint collections of math texts out there, I wish them the best in publishing new works with the same quality and great prices as they always have! We need more publishers like this.

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🔖 Free download of Quantum Theory, Groups and Representations: An Introduction by Peter Woit

🔖 Free download of Quantum Theory, Groups and Representations: An Introduction by Peter Woit
Final Draft of Quantum Theory, Groups and Representations: An Introduction by Peter Woit(Not Even Wrong | math.columbia.edu)

Final Draft Version

http://www.math.columbia.edu/~woit/wordpress/?p=8844&embed=true#?secret=nM1mFEstsw

Peter Woit has just made the final draft (dated 10/25/16) of his new textbook Quantum Theory, Groups and Representations: An Introduction freely available for download from his website. It covers quantum theory with a heavy emphasis on groups and representation theory and “contains significant amounts of material not well-explained elsewhere.” He expects to finish up the diagrams and publish it next year some time, potentially through Springer.

I finally have finished a draft version of the book that I’ve been working on for the past four years or so. This version will remain freely available on my website here. The plan is to get professional illustrations done and have the book published by Springer, presumably appearing in print sometime next year. By now it’s too late for any significant changes, but comments, especially corrections and typos, are welcome.

At this point I’m very happy with how the book has turned out, since I think it provides a valuable point of view on the relation between quantum mechanics and mathematics, and contains significant amounts of material not well-explained elsewhere.

Peter Woit (September 11, 1957— ), theoretical physicist, mathematician, professor Department of Mathematics, Columbia University
in Final Draft Version | Not Even Wrong

 

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🔖 Advanced Data Analysis from an Elementary Point of View by Cosma Rohilla Shalizi

Advanced Data Analysis from an Elementary Point of View
by Cosma Rohilla Shalizi

This is a draft textbook on data analysis methods, intended for a one-semester course for advance undergraduate students who have already taken classes in probability, mathematical statistics, and linear regression. It began as the lecture notes for 36-402 at Carnegie Mellon University.

By making this draft generally available, I am not promising to provide any assistance or even clarification whatsoever. Comments are, however, welcome.

The book is under contract to Cambridge University Press; it should be turned over to the press before the end of 2015. A copy of the next-to-final version will remain freely accessible here permanently.

Complete draft in PDF

Table of contents:

    I. Regression and Its Generalizations

  1. Regression Basics
  2. The Truth about Linear Regression
  3. Model Evaluation
  4. Smoothing in Regression
  5. Simulation
  6. The Bootstrap
  7. Weighting and Variance
  8. Splines
  9. Additive Models
  10. Testing Regression Specifications
  11. Logistic Regression
  12. Generalized Linear Models and Generalized Additive Models
  13. Classification and Regression Trees
    II. Distributions and Latent Structure
  14. Density Estimation
  15. Relative Distributions and Smooth Tests of Goodness-of-Fit
  16. Principal Components Analysis
  17. Factor Models
  18. Nonlinear Dimensionality Reduction
  19. Mixture Models
  20. Graphical Models
    III. Dependent Data
  21. Time Series
  22. Spatial and Network Data
  23. Simulation-Based Inference
    IV. Causal Inference
  24. Graphical Causal Models
  25. Identifying Causal Effects
  26. Causal Inference from Experiments
  27. Estimating Causal Effects
  28. Discovering Causal StructureAppendices
    • Data-Analysis Problem Sets
    • Reminders from Linear Algebra
    • Big O and Little o Notation
    • Taylor Expansions
    • Multivariate Distributions
    • Algebra with Expectations and Variances
    • Propagation of Error, and Standard Errors for Derived Quantities
    • Optimization
    • chi-squared and the Likelihood Ratio Test
    • Proof of the Gauss-Markov Theorem
    • Rudimentary Graph Theory
    • Information Theory
    • Hypothesis Testing
    • Writing R Functions
    • Random Variable Generation

Planned changes:

  • Unified treatment of information-theoretic topics (relative entropy / Kullback-Leibler divergence, entropy, mutual information and independence, hypothesis-testing interpretations) in an appendix, with references from chapters on density estimation, on EM, and on independence testing
  • More detailed treatment of calibration and calibration-checking (part II)
  • Missing data and imputation (part II)
  • Move d-separation material from “causal models” chapter to graphical models chapter as no specifically causal content (parts II and IV)?
  • Expand treatment of partial identification for causal inference, including partial identification of effects by looking at all data-compatible DAGs (part IV)
  • Figure out how to cut at least 50 pages
  • Make sure notation is consistent throughout: insist that vectors are always matrices, or use more geometric notation?
  • Move simulation to an appendix
  • Move variance/weights chapter to right before logistic regression
  • Move some appendices online (i.e., after references)?

(Text last updated 30 March 2016; this page last updated 6 November 2015)

🔖 Advanced Data Analysis from an Elementary Point of View by Cosma Rohilla Shalizi was originally published on Chris Aldrich

Network Science by Albert-László Barabási

Network Science by Albert-László Barabási
Network Science by Albert-László BarabásiAlbert-László Barabási(Cambridge University Press)

I ran across a link to this textbook by way of a standing Google alert, and was excited to check it out. I was immediately disappointed to think that I would have to wait another month and change for the physical textbook to be released, but made my pre-order directly. Then with a bit of digging around, I realized that individual chapters are available immediately to quench my thirst until the physical text is printed next month.

The power of network science, the beauty of network visualization.

Network Science, a textbook for network science, is freely available under the Creative Commons licence. Follow its development on Facebook, Twitter or by signing up to our mailing list, so that we can notify you of new chapters and developments.

The book is the result of a collaboration between a number of individuals, shaping everything, from content (Albert-László Barabási), to visualizations and interactive tools (Gabriele Musella, Mauro Martino, Nicole Samay, Kim Albrecht), simulations and data analysis (Márton Pósfai). The printed version of the book will be published by Cambridge University Press in 2016. In the coming months the website will be expanded with an interactive version of the text, datasets, and slides to teach the material.

Book Contents

Personal Introduction
1. Introduction
2. Graph Theory
3. Random Networks
4. The Scale-Free Property
5. The Barabási-Albert Model
6. Evolving Networks
7. Degree Correlations
8. Network Robustness
9. Communities
10. Spreading Phenomena
Usage & Acknowledgements
About

Albert-László Barabási
on Network Science (book website)

Networks are everywhere, from the Internet, to social networks, and the genetic networks that determine our biological existence. Illustrated throughout in full colour, this pioneering textbook, spanning a wide range of topics from physics to computer science, engineering, economics and the social sciences, introduces network science to an interdisciplinary audience. From the origins of the six degrees of separation to explaining why networks are robust to random failures, the author explores how viruses like Ebola and H1N1 spread, and why it is that our friends have more friends than we do. Using numerous real-world examples, this innovatively designed text includes clear delineation between undergraduate and graduate level material. The mathematical formulas and derivations are included within Advanced Topics sections, enabling use at a range of levels. Extensive online resources, including films and software for network analysis, make this a multifaceted companion for anyone with an interest in network science.

Source: Cambridge University Press

The textbook is available for purchase in September 2016 from Cambridge University Press. Pre-order now on Amazon.com.

If you’re not already doing so, you should follow Barabási on Twitter.

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