Article and Book References
I do not provide links to Amazon, Google, Abe Books, etc., but these usually appear on the WorldCat listing with pricing when available. See at bottom for ethically searching for open access digital resources.
I am a registered affiliate with Bookshop.org; purchase proceeds will be shared with me to help support my curation efforts.
I also accept, and greatly appreciate, donations at my Ko-fi page. Thank you!
Index
Algebra
Analysis
Approximation
Category Theory
History
Logic
Machine Learning
Philosophy
- Aluffi, Paolo
- Algebra: Notes from the Underground, Cambridge University Press, 2021
- Awodey, Steve
- Structure in Mathematics and Logic: A Categorical Perspective, Philosophia Mathematica, Vol. 4, No. 3, 1996
- Category Theory, Oxford University Press, 2010
- Avigad, Jeremy
- Mathematical Logic and Computation, Cambridge University Press, 2023
- Bishop and Bishop
- Deep Learning: Foundations and Concepts, Springer, 2023
- Boolos, George
- The Iterative Conception of Set, Journal of Philosphy, Vol. 68, 1971
- Bell, John L
- A Primer of Infinitesimal Analysis, Cambridge University Press, 1998
- Category Theory and the Foundations of Mathematics, British Journal for the Philosophy of Science, Vol. 32, No. 4, 1981
- Toposes and Local Set Theories: An Introduction, Dover Publications, 2008
- Bernays, Paul
- A System of Axiomatic Set Theory, Part III, Journal of Symbolic Logic, Vol. 7 No 2, 1942
- Bishop, Erret
- Foundations of Constructive Analysis, McGraw-Hill, 1967
- Cohen, Paul J
- Set Theory and the Continuum Hypothesis, Dover Publications, 2008
- Diaconescu, Radu
- Axiom of Choice and Complementation, Proceedings of the American Mathematical Society, Vol. 51, 1975
- Dummett, Michael
- The Philosophical Basis of Intuitionistic Logic, Proceedings of the Logic Colloquium 1973, Studies in Logic and the Foundations of Mathematics, Vol. 80, 1975
- Ewald, William
- From Kant to Hilbert: A Source Book in the Foundations of Mathematics, Vol 1, Oxford University Press, 1999
- From Kant to Hilbert: A Source Book in the Foundations of Mathematics, Vol 2, Oxford University Press, 1999
- Friedman and Mendhekar
- The Little Learner: A Straight Line to Deep Learning, MIT Press, 2023
- Goodfellow, Bengio, and Courville
- Deep Learning, MIT Press, 2016
- Gödel, Kurt
- The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis, Institute for Advanced Study, Princeton University, 1938
- Consistency of the Continuum Hypothesis, Princeton University Press, 1940
- Lambek and Scott
- Introduction to Higher-Order Categorical Logic, Cambridge University Press
- Landry, Elaine
- Categories for the Working Philosopher, Oxford University Press, 2017
- Lang, Serge
- Undergraduate Analysis, Springer, 2010
- Lawvere, F. William
- An Elementary Theory of the Category of Sets (Long Version), Reprints in Theory and Applications of Categories, No. 12, 2005
- Leinster, Tom
- Rethinking Set Theory, American Mathematical Monthly, Vol 121, No 5, 2014
- Linnebo, Øystein
- Philosophy of Mathematics, Princeton University Press, 2017
- Linnebo and Pettigrew
- Category Theory as an Autonomous Foundation, Philosophia Mathematica, Vol 13, No 3, 2011
- Mancosu, Paolo
- The Philosophy of Mathematical Practice, Oxford University Press, 2011
- Maddy, Penelope
- Believing the Axioms (1), Journal of Symbolic Logic, Vol. 53, No. 2, 1988
- Believing the Axioms (2), Journal of Symbolic Logic, Vol. 53. No. 3, 1988
- Naturalism in Mathematics, Oxford University Press, 1997
- Defending the Axioms, Oxford University Press, 2011
- Mayers and Süli
- An Introduction to Numerical Analysis, Cambridge University Press, 2003
- McLarty, Colin
- On the Uses and Abuses of the History of Topos Theory, The British Journal for the Philosophy of Science, Vol 41, No 3, 1990
- Numbers Can Be Just What They Have To, Noûs, Vol. 27, No. 4, 1993
- Categorical Foundations and Mathematical Practice, Philosophica Mathematica, Vol. 20, No. 1, 2012
- Moore, Gregory H
- Zermelo's Axiom of Choice: It's Origins, Development, and Influence, Dover Publications, 2013
- Osius, Gerhard
- Categorical Set Theory: A Characterization of the Category of Sets, Journal of Pure and Applied Algebra, Vol. 4, No. 1, 1974
- Powell, M.J.D.
- Approximation Theory and Methods, Cambridge University Press, 1981
- Rosiak, Daniel
- Sheaf Theory through Examples, MIT Press, 2022
- Rudin, Walter
- Principles of Mathematical Analysis, Springer, 2010
- Sally, Paul J
- Tools of the Trade: Introduction to Advanced Mathematics, American Mathematical Society, 2008
- Smullyan, Raymond
- Gödel's Incompleteness Theorems, Oxford University Press, 2020
- First-Order Logic, Dover Publications, 1995
- Smullyan and Fitting
- Set Theory and the Continuum Problem, Dover Publications, 2010
- Tait, William Weaver
- Frege versus Cantor and Dedekind: On the concept of number
- Troelstra, Anne S
- Aspects of Constructive Mathematics, Studies in Logic and the Foundations of Mathematics, Vol. 90, 1977
- Troelstra and van Dalen
- Constructivism in Mathematics: An Introduction, Elsevier Science, 1988
- Univalent Foundations Program
- Homotopy Type Theory: Univalent Foundations of Mathematics, Institute for Advanced Study, Princeton University, 2013
- Wilson, Robin
- Four Colors Suffice, Princeton University Press, 2013
How to Find Open Access Publications
You should not pirate content; besides being illegal, piracy cheats the authors, editors, and publishers who work to make the content available.
There's a good argument that knowledge should be open access. Yet this requires consent from the copyright owners. While it's true that universities and publishers have been slow to make open access a reality in our increasingly information-based society, that does not mean sluggishness justifies theft.
The instructions I give below provide an ethical approach to finding and accessing texts without personal cost - or liability.
I recommend the following phases in searching for an open access publication.
- Search arXiv. Many working scientific authors place "pre-prints" on arXiv prior to gaining publication in journals or presses. This will not work for historical texts.
- Search WorldCat. Public libraries and local college libraries often have large collections. Sometimes, your library branch may be part of a consortium of libraries or an open licensing deal with a publisher. By using a library, your patronage contributes data for funding the library's collections and activities, potentially expanding access in the future.
- Check the publisher's website. A number of academic publishers have made good efforts in recent years to open up their catalogs. The ones I examine most frequently are
- oapen.org — try this one first; some catalogs below feed into the oapen database.
- Cambridge University Press
- Oxford University Press
- University of Chicago Press
- MIT Press
- Search Kagi, an alternative, advertisement-free search engine. Kagi search allows you to restrict the scope to an academic website index, avoiding pirates and scammers.
- If you currently attend an academic institution as a student, if you work as academic faculty or staff, or if you're an alumnus, you may have additional, non-public access rights through your school's library. A consortium such as Sibboleth may allow you to log into your school-linked account and access certain resources. Again, you should think of this option as another patronage action, helping fund the consortium via fees paid by your school library.
- Check the author's personal website. Academic authors, especially, enter into agreements with their publishers to host pre-prints or updates on their own server. On occasion, you may try emailing the author; but I advise doing this only as a last resort and only if you legitimately do not have the means to purchase an available copy.
I do not include Internet Archive above as they're currently under litigation for copyright violations. While Internet Archive does host some high quality scans from historical sources, given that the donations generally come from accredited libraries, I strongly recommend option (2) above instead. Opinions differ, of course, and this is merely my opinion.