Resources

Compiled by your fellow Academy students, this list provides valuable resources for learning beyond the standard curriculum. This list is updated regularly. We would appreciate you submitting contributions via the suggestions form on the homepage.

General:

• MIT OpenCourseWare

  • MIT OpenCourseWare makes the materials used in the teaching of almost all of MIT's subjects available on the Web, free of charge. More than 2,400 courses are available.

• arXiv

  • arXiv is a free distribution service and an open-access archive for 1,696,911+ scholarly articles in the fields of physics, mathematics, computer science, quantitative biology, quantitative finance, statistics, electrical engineering and systems science, and economics.

• nLab

  • We all make notes as we read papers, read books and doodle on pads of paper. The nLab is somewhere to put all those notes, and, incidentally, to make them available to others. Others might read them and add or polish them. But even if they don’t, it is still easier to link from them to other notes that you’ve made.

• The Chicago Manual of Style

  • One of the most widely used and respected style guides in the United States. Specifically focuses on American English and deals with aspects of editorial practice, including grammar and usage, as well as document preparation and formatting.

Mathematics:

• NOTE: The following are sorted by topic, then by difficulty.

• AMS Open Math Notes

• 2018 Putnam Problems

• MIT PRIMES Problems 2020

  • Entrance exam for the most rigorous research mentorship program available to high school students. Problems are published ~2.5 months before the due date. You are encouraged to apply if you can solve at least 50% of the problems.

• Calculus Early Transcendentals (James Stewart)

• Calculus a Modern Approach (Jeff Knisley and Kevin Shirley)

• Calculus (Gilbert Strang)

• Single and Multivariable Calculus (David Guichard, Neal Koblitz, H. Jerome Keisler)

• Advanced Calculus (Lynn H. Loomis and Shlomo Sternberg)

• A First Course in Linear Algebra (Robert A. Beezer)

• Applied Linear Algebra (Stephen Boyd and Lieven Vanderberghe)

• Linear Algebra (David Cherney, Tom Denton, Rohit Thomas and Andrew Waldron)

• THE BOOK OF PROOF (add link)

  • Gives students the confidence to begin proving conjectures. This skill is essential for further studies in mathematics.

• A Course in Real Analysis ( P. Kronheimer)

• Understanding Analysis (Stephen Abbott)

  • More verbose (and therefore accessible) than Rudin. Recommended as a first introduction to real analysis.

• Principles of Mathematical Analysis (Walter Rudin)

  • Affectionately known as "Baby Rudin" (preceding "Big Rudin" and "Grandpa Rudin"), this book sets the standard for undergraduate real analysis texts. Exercises are rich and challenging, and proofs are minimalist and to the point. However, the book earned its reputation in 1953, and many contend that modern texts like Abbott's are pedagogically superior. Still, it would be remiss not to include it here as it is a classic.

  • Community-written solution manual

• Abstract Algebra (Dummit and Foote)

  • Comprehensive reference for algebraic topics. Typically used at advanced undergraduate or graduate level. Particularly suited to self-study because of its copious examples and plethora of exercises.

• Topology (James Munkres)

  • Standard undergraduate/early graduate text in point-set topology. Later parts provide a solid introduction to algebraic topology.

Literature:

• Project Gutenberg

  • A library of over 60,000 free eBooks. Choose among free epub and Kindle eBooks, download them or read them online. You will find the world's great literature here, with focus on older works for which U.S. copyright has expired. Thousands of volunteers digitized and diligently proofread the eBooks, for enjoyment and education.

• http://penelope.uchicago.edu/

• Letter from a Region in My Mind (James Baldwin)

• The Dream of the Red Chamber (Cao Xueqin)

• Heart of Darkness (Joseph Conrad)

• Anna Karenina (Leo Tolstoy)

• A Narrative of the Most Remarkable Particulars in the Life of James Albert Ukawsaw Gronniosaw, an African Prince, as Related by Himself

• A Modest Proposal (Jonathan Swift)

• Waiting for God (Simone Weil)

• Descartes' Meditations

• The "Art" of Rhetoric (Aristotle)

History:

• The Avalon Project: Documents in Law, History, and Diplomacy

  • Extensive database of historical documents

• American Rhetoric

• Sinners in the Hands of an Angry God (Jonathan Edwards)

• The War With Catiline (Sallust)

• The Annals (Tacitus)

• Michael Psellos

Physics:

• https://myphysicslab.com/index-en.html

  • A series of interesting simulations of various physical systems. Highly customizable. Provides graphs.

• The Physics Hypertextbook

  • Physics boiled down to the essentials, in a hyperlinked website format (hence the name). Very useful for a quick explanation or derivation.

• The Theoretical Minimum

  • A series of Stanford Continuing Studies courses taught by world-renowned physicist Leonard Susskind. These courses collectively teach everything required to gain a basic understanding of each area of modern physics, including all of the fundamental mathematics.

• Griffiths (ADD LINK)

  • ubiquitous in junior-level E&M courses.

• Classical Electrodynamics (Jackson)

  • The most difficult physics book in the history of anything ever. Or something like that. Apparently an infamous rite of passage for graduate students in physics.

• Classical Mechanics (Peter Dourmashkin)

• Classical Mechanics (John R. Taylor)

• Smooth Bore Cannon Ballistics

• Solitons

Chemistry:

• Chemistry (Zumdahl et al.)

  • Apparently a decent general chemistry textbook. Probably useful for AP Chemistry.