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Resources

Level: reference · for finding the books and talks this library leans on

One line: The outside sources behind the pages, grouped by what they are for, each with the page that uses it.

A page here cites its sources in its own See also; this page gathers the main ones in one place. It is not a reading list for mathematics in general: every entry is here because a page uses it.

Learning how to learn

These books now belong to the Learning to Learn library ↗, whose resources ↗ and references ↗ pages carry them on; the list stays here because the chapter began in this repo.

  • Saundra Yancy McGuire with Stephanie McGuire, Teach Yourself How to Learn: Strategies You Can Use to Ace Any Course at Any Level (Stylus, 2018), foreword by Mark McDaniel. The book behind 12_Learning_to_Learn ↗: metacognition and Flavell's four abilities (chapter 3, Figure 3.2), the Count the Vowels exercise (Figure 3.3), studying versus learning, Bloom's taxonomy and the study cycle with intense study sessions (chapter 4). Short, practical, and written for students; start here.
  • Peter C. Brown, Henry L. Roediger III and Mark A. McDaniel, Make It Stick: The Science of Successful Learning (Harvard University Press, 2014). The research on retrieval practice, spacing and interleaving, told for a general reader. McGuire recommends it as a place to start on the science; used in spaced retrieval ↗.
  • John Medina, Brain Rules (Pear Press, 2008). McGuire's other recommendation on the cognitive science of memory, cited for reviewing soon after class.
  • Terry Doyle and Todd Zakrajsek, The New Science of Learning: How to Learn in Harmony With Your Brain (Stylus, 2013). Cited by McGuire for breaks, rest and naps after learning. The third edition, by Todd Zakrajsek alone (Stylus/Routledge, 2022), is the source of these pages: from chapter 1, "Learning from Multiple Perspectives", day or night: perspective taking ↗; from chapter 2, "Discovering Yourself as a Learner", learned helplessness ↗ and the summary of self-regulation and self-efficacy ↗; from chapter 3, "Developing Your Learning Strategy", the buffer hour ↗ and the summary of goals and schedules ↗; from chapter 4, "Improving the Learning Process", and chapter 6, "Finding and Using Patterns", cognitive load ↗, interleaving ↗ and the summary of how learning and memory work ↗; from chapter 5, "Exploring Social Influences", the mindset steps and the two biases under motivation ↗ and the planning, monitoring and evaluating added to metacognition ↗.
  • Martin Seligman, Learned Optimism: How to Change Your Mind and Your Life (1990). The book that turned the study of learned helplessness ↗ round into positive psychology; the source of the three Ps of pessimism.
  • Carol S. Dweck, Mindset: The New Psychology of Success (Random House, 2006). Fixed and growth mindsets: whether you believe ability can be developed changes how you meet challenges, setbacks, effort and criticism. McGuire's chapter 6 builds on it, including a section on stereotypes about mathematical ability. Later large studies found the effect of mindset interventions on grades real but small, so it is best read as one ingredient, not the whole recipe.
  • Susan A. Ambrose and others, How Learning Works: Seven Research-Based Principles for Smart Teaching (Jossey-Bass, 2010). Written for teachers, useful to learners. McGuire's chapter 7 takes from it the three levers of motivation: the value of the goal, whether the environment feels supportive, and belief in the ability to succeed. Its chapter on how students organise knowledge is the research behind count the vowels ↗.
  • Lorin W. Anderson and David R. Krathwohl (eds.), A Taxonomy for Learning, Teaching, and Assessing (Longman, 2001). The revised Bloom's taxonomy, used in studying vs learning ↗.
  • Henry L. Roediger III and Jeffrey D. Karpicke, "Test-enhanced learning", Psychological Science 17 (2006). The experiment in which rereaders felt surer and remembered less; used in metacognition ↗.
  • Barbara Oakley, A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra) (TarcherPerigee, 2014). Focused and diffuse thinking, and why stepping away from a stuck problem helps: the break in McGuire's intense study session, explained. Written for exactly the reader of this library.
  • Barbara Oakley, Terrence Sejnowski and Alistair McConville, Learning How to Learn: How to Succeed in School Without Spending All Your Time Studying; A Guide for Kids and Teens (TarcherPerigee, 2018). The ideas of A Mind for Numbers retold for younger readers, with cartoons: chapter 2, "Easy Does It", is the source of focused and diffuse thinking ↗, which also maps the rest of the book to the lessons here.
  • Learning How to Learn ↗, a free Coursera course by Barbara Oakley and Terrence Sejnowski: the same ideas as A Mind for Numbers, in short videos, with a section on procrastination.
  • Scott H. Young, Ultralearning (Harper Business, 2019). Self-directed, project-based learning of hard skills, with retrieval and feedback at its centre. Useful for working through a whole book or subject, such as a chapter here, on your own.
  • Huberman Lab podcast, Andrew Huberman's episodes on focus and on neuroplasticity: the biology of attention and learning, told at length for a general audience. Background rather than method.
  • John Dunlosky, "Strengthening the student toolbox: study strategies to boost learning", American Educator (2013), free from the AFT ↗. A teacher-friendly summary of a large review of ten study techniques. Practice testing and spaced (distributed) practice come out most useful; highlighting and rereading, the two most popular, come out least. It is the short evidence behind spaced retrieval ↗ and metacognition ↗.
  • Pam A. Mueller and Daniel M. Oppenheimer, "The pen is mightier than the keyboard", Psychological Science 25 (2014). The study behind McGuire's advice to take class notes by hand: typists copied the lecture word for word, and those who wrote by hand had to put it in their own words. A 2019 replication (Morehead, Dunlosky and Rawson) found the advantage smaller and less certain.
  • Saundra Yancy McGuire, Teach Students How to Learn (Stylus, 2015). The companion book for teachers, and Cook, Kennedy and McGuire, "Effect of teaching metacognitive learning strategies on performance in general chemistry courses", Journal of Chemical Education 90 (2013), the classroom evidence she draws on.
  • Study tools, from McGuire's appendix: flashcards (by hand, or apps such as Quizlet), colour highlighting, mnemonics (ROYGBIV), a timer for intense study sessions (such as a Pomodoro timer), note-taking systems (Cornell notes), concept and mind maps, study guides as outlines or charts, and quiz-making apps. Her advice is to experiment until something works, and she endorses no particular tool. Read it beside Dunlosky: a tool that makes you answer beats one that makes you look.
  • Learning with AI. Hamsa Bastani and colleagues, "Generative AI without guardrails can harm learning: evidence from high school mathematics", PNAS (2025), and Gregory Kestin and colleagues, "AI tutoring outperforms in-class active learning", Scientific Reports (2025): the two field studies behind the Learning with AI ↗ section.
  • McGuire's own further reading, beyond the books above: David Ellis, Becoming a Master Student (Cengage, 2014), and John N. Gardner and Betsy O. Barefoot, Your College Experience: Strategies for Success, 12th ed. (Macmillan, 2016), both general guides to studying in college. Her appendix also points to websites, listed here as the 2018 book prints them, so some may have moved: mindsetonline.com ↗ to assess your mindset, howtostudy.org ↗ for test preparation, LSU's Center for Academic Success ↗, where her study cycle comes from, and drearlbloch.com ↗ for learning, study and testing strategies, and a relaxation-techniques guide from UC Davis for stress relief.
  • Anki ↗, the free flashcard program that reads the decks on this library's pages, and SuperMemo's SM-2 ↗, the scheduling algorithm it started from.

Textbooks the pages read

  • Michael Sullivan, Precalculus (Pearson). Chapter 1 is 08_Analytic_Geometry, its review appendix is 10_Geometry, and the precalculus reading guide sets it beside the alternatives.
  • Jim Hefferon, Linear Algebra ↗, free. Its first section is 07_Linear_Systems; the linear algebra reading guide compares it with Strang and Axler.
  • René Cori and Daniel Lascar, Mathematical Logic: A Course with Exercises, Part II (Oxford, 2001), chapter 7; Daniel W. Cunningham, Set Theory: A First Course (Cambridge, 2016), chapter 1; Thomas Jech, Set Theory, third millennium edition (Springer, 2003), chapters 1 and 2; Kenneth Kunen, The Foundations of Mathematics (College Publications, 2009), chapter I. Behind 13_Axioms_of_Set_Theory and the two new lessons of 11_Logic; the set theory reading guide places them among the other books, with the founding papers.
  • Jean-Michel Muller and others, Handbook of Floating-Point Arithmetic (Birkhäuser). Behind 01_Precision, and the source of the doors its roadmap entry leaves open.
  • David Thrane Christiansen, Functional Programming in Lean ↗ (Microsoft 2023, Lean FRO, CC BY 4.0, free). The Lean reading guide reads its introduction and interludes from the source, runs Lean's definitions of And, Or, Not and Set as a program, and places Theorem Proving in Lean 4, Mathematics in Lean and Lean Beam beside it.
  • Lawrence C. Paulson, Isabelle's Logics: FOL and ZF (with Tobias Nipkow and Markus Wenzel; the manual shipped with Isabelle, free ↗). The proof assistants reading guide places it, sets its ZF axioms beside 13_Axioms_of_Set_Theory, and runs its powerset proof against a model check.

Talks

  • Grant Sanderson (3Blue1Brown) on e^{iπ} = −1. Euler's formula: a lesson plan maps each screen of the talk to the lesson that explains it, and 09_Calculus tells calculus as motion, the way the talk does.

Auf Deutsch: Stichwörter

Die Bücher, Vorträge und Werkzeuge hinter den Lektionen, mit dem Kapitel, das aus jedem entstand.

Stichwörter: Quellen, Lehrbuch (textbook), Vortrag (talk), Werkzeug (tool), Lesehilfe, frei verfügbar (free).