Bibliography
- Page ID
- 50984
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Aspray, William. 1984. The Princeton Mathematics Community in the 1930s: Alonzo Church. URL http://www.princeton.edu/mudd/findin...oral/pmc05.htm. Interview.
Baaz, Matthias, Christos H. Papadimitriou, Hilary W. Putnam, Dana S. Scott, and Charles L. Harper Jr. 2011. Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge: Cambridge University Press.
Benacerraf, Paul. 1965. What numbers could not be. The Philosophical Review 74(1): 47–73.
Cantor, Georg. 1892. Über eine elementare Frage der Mannigfaltigkeitslehre. Jahresbericht der deutschen Mathematiker-Vereinigung 1: 75–8.
Cheng, Eugenia. 2004. How to write proofs: A quick guide. URL http://cheng.staff.shef.ac.uk/proofg...proofguide.pdf.
Church, Alonzo. 1936a. A note on the Entscheidungsproblem. Journal of Symbolic Logic 1: 40–41.
Church, Alonzo. 1936b. An unsolvable problem of elementary number theory. American Journal of Mathematics 58: 345–363.
Corcoran, John. 1983. Logic, Semantics, Metamathematics. Indianapolis: Hackett, 2nd ed.
Dauben, Joseph. 1990. Georg Cantor: His Mathematics and Philosophy of the Infinite. Princeton: Princeton University Press.
Dick, Auguste. 1981. Emmy Noether 1882–1935. Boston: Birkhäuser.
du Sautoy, Marcus. 2014. A brief history of mathematics: Georg Cantor. URL http://www.bbc.co.uk/programmes/b00ss1j0. Audio Recording.
Duncan, Arlene. 2015. The Bertrand Russell Research Centre. URL http://russell.mcmaster.ca/.
Ebbinghaus, Heinz-Dieter. 2015. Ernst Zermelo: An Approach to his Life and Work. Berlin: Springer-Verlag.
Ebbinghaus, Heinz-Dieter, Craig G. Fraser, and Akihiro Kanamori. 2010. Ernst Zermelo. Collected Works, vol. 1. Berlin: Springer-Verlag.
Ebbinghaus, Heinz-Dieter and Akihiro Kanamori. 2013. Ernst Zermelo: Collected Works, vol. 2. Berlin: Springer-Verlag.
Enderton, Herbert B. 2019. Alonzo Church: Life and Work. In The Collected Works of Alonzo Church, eds. Tyler Burge and Herbert B. Enderton. Cambridge, MA: MIT Press.
Feferman, Anita and Solomon Feferman. 2004. Alfred Tarski: Life and Logic. Cambridge: Cambridge University Press.
Feferman, Solomon, John W. Dawson Jr., Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay, and Jean van Heijenoort. 1986. Kurt Gödel: Collected Works. Vol. 1: Publications 1929–1936. Oxford: Oxford University Press.
Feferman, Solomon, John W. Dawson Jr., Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay, and Jean van Heijenoort. 1990. Kurt Gödel: Collected Works. Vol. 2: Publications 1938–1974. Oxford: Oxford University Press.
Frege, Gottlob. 1884. Die Grundlagen der Arithmetik: Eine logisch mathematische Untersuchung über den Begriff der Zahl. Breslau: Wilhelm Koebner. Translation in Frege (1953).
Frege, Gottlob. 1953. Foundations of Arithmetic, ed. J. L. Austin. Oxford: Basil Blackwell & Mott, 2nd ed.
Frey, Holly and Tracy V. Wilson. 2015. Stuff you missed in history class: Emmy Noether, mathematics trailblazer. URL http://www.missedinhistory.com/podca...s-trailblazer/. Podcast audio.
Gentzen, Gerhard. 1935a. Untersuchungen über das logische Schließen I. Mathematische Zeitschrift 39: 176–210. English translation in Szabo (1969), pp. 68–131.
Gentzen, Gerhard. 1935b. Untersuchungen über das logische Schließen II. Mathematische Zeitschrift 39: 176–210, 405–431. English translation in Szabo (1969), pp. 68–131.
Gödel, Kurt. 1929. Über die Vollständigkeit des Logikkalküls [On the completeness of the calculus of logic]. Dissertation, Universität Wien. Reprinted and translated in Feferman et al. (1986), pp. 60–101.
Gödel, Kurt. 1931. über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I [On formally undecidable propositions of Principia Mathematica and Related Systems I]. Monatshefte für Mathematik und Physik 38: 173–198. Reprinted and translated in Feferman et al. (1986), pp. 144–195.
Grattan-Guinness, Ivor. 1971. Towards a Biography of Georg Cantor. Annals of Science 27(4): 345–391.
Hammack, Richard. 2013. Book of Proof. Richmond, VA: Virginia Commonwealth University. URL http://www.people.vcu.edu/~rhammack/...ookOfProof.pdf.
Hodges, Andrew. 2014. Alan Turing: The Enigma. London: Vintage.
Hutchings, Michael. 2003. Introduction to mathematical arguments. URL https://math.berkeley.edu/~hutching/teach/proofs.pdf.
Institute, Perimeter. 2015. Emmy Noether: Her life, work, and influence. URL https://www.youtube.com/watch?v=tNNyAyMRsgE. Video Lecture.
Irvine, Andrew David. 2015. Sound clips of Bertrand Russell speaking. URL http://plato.stanford.edu/entries/ru...oundclips.html.
Jacobson, Nathan. 1983. Emmy Noether: Gesammelte Abhandlungen–Collected Papers. Berlin: Springer-Verlag.
John Dawson, Jr. 1997. Logical Dilemmas: The Life and Work of Kurt Gödel. Boca Raton: CRC Press.
LibriVox. n.d. Bertrand Russell. URL https://librivox.org/author/1508?pri...rm=get_results. Collection of public domain audiobooks.
Linsenmayer, Mark. 2014. The partially examined life: Gödel on math. URL http://www.partiallyexaminedlife.com...16/ep95-godel/. Podcast audio.
MacFarlane, John. 2015. Alonzo Church's JSL Reviews. URL http://johnmacfarlane.net/church.html.
Menzler-Trott, Eckart. 2007. Logic's Lost Genius: The Life of Gerhard Gentzen. Providence: American Mathematical Society.
Potter, Michael. 2004. Set Theory and its Philosophy. Oxford: Oxford University Press.
Radiolab, 2012. The Turing problem. URL http://www.radiolab.org/story/193037-turing-problem/. Podcast audio.
Rose, Daniel. 2012. A song about Georg Cantor. URL https://www.youtube.com/watch?v=QUP5Z4Fb5k4. Audio Recording.
Russell, Bertrand. 1905. On denoting. Mind 14: 479–493.
Russell, Bertrand. 1967. The Autobiography of Bertrand Russell, vol. 1. London: Allen and Unwin.
Russell, Bertrand. 1968. The Autobiography of Bertrand Russell, vol. 2. London: Allen and Unwin.
Russell, Bertrand. 1969. The Autobiography of Bertrand Russell. vol. 3. London: Allen and Unwin.
Russell, Bertrand. n.d. Bertrand Russell on smoking. URL https://www.youtube.com/watch?v=80oLTiVW_lc. Video Interview.
Sandstrum, Ted. 2019. Mathematical Reasoning: Writing and Proof. Allendale, MI: Grand Valley State University. URL https://scholarworks.gvsu.edu/books/7/.
Segal, Sanford L. 2014. Mathematicians under the Nazis. Princeton: Princeton University Press.
Sigmund, Karl, John Dawson, Kurt Mühlberger, Hans Magnus Enzensberger, and Juliette Kennedy. 2007. Kurt Gödel: Das Album–The Album. The Mathematical Intelligencer 29(3): 73–76.
Smith, Peter. 2013. An Introduction to Gödel's Theorems. Cambridge: Cambridge University Press.
Solow, Daniel. 2013. How to Read and Do Proofs. Hoboken, NJ: Wiley.
Steinhart, Eric. 2018. More Precisely: The Math You Need to Do Philosophy. Peterborough, ON: Broadview, 2nd ed.
Sykes, Christopher. 1992. BBC Horizon: The strange life and death of Dr. Turing. URL https://www.youtube.com/watch?v=gyusnGbBSHE.
Szabo, Manfred E. 1969. The Collected Papers of Gerhard Gentzen. Amsterdam: North-Holland.
Takeuti, Gaisi, Nicholas Passell, and Mariko Yasugi. 2003. Memoirs of a Proof Theorist: Gödel and Other Logicians. Singapore: World Scientific.
Tarski, Alfred. 1981. The Collected Works of Alfred Tarski, vol. I–IV. Basel: Birkhäuser.
Theelen, Andre. 2012. LEGO turing machine. URL https://www.youtube.com/watch?v=FTSAiF9AHN4.
Turing, Alan M. 1937. On computable numbers, with an application to the “Entscheidungsproblem”. Proceedings of the London Mathematical Society, 2nd Series 42: 230–265.
Tyldum, Morten. 2014. The imitation game. Motion picture.
Velleman, Daniel J. 2019. How to Prove It: A Structured Approach. Cambridge: Cambridge University Press, 3rd ed.
Wang, Hao. 1990. Reflections on Kurt Gödel. Cambridge: MIT Press.
Zermelo, Ernst. 1904. Beweis, daß jede Menge wohlgeordnet werden kann. Mathematische Annalen 59: 514–516. English translation in (Ebbinghaus et al., 2010, pp. 115–119).
Zermelo, Ernst. 1908. Untersuchungen über die Grundlagen der Mengenlehre I. Mathematische Annalen 65(2): 261–281. English translation in (Ebbinghaus et al., 2010, pp. 189-229).