Foundations draft

Foundations

This section is for housing material that is prerequisite to taking certain courses in computer science. The material does not directly fall into the computer science field, and you should utilize it only as needed based on your level and background.

K-8 Math

Prerequisites

• None

Resources

Format	Resource	Use cases
course	Khan Academy Math K-8	learn

Needed by

• High School Math

High School Math

Prerequisites

• K-8 Math

Resources

Format	Resources	Use cases
course	Khan Academy: High school math (all sections)	learn
course	ASU College Algebra and Problem Solving	practice review
course	ASU Precalculus	practice review
forum	/r/learnmath	help

Needed by

• Single-variable Calculus
• Linear Algebra (Beginner track)

Single-variable Calculus

The best online courses for this subject are MIT Calculus 1A through 1C. If you prefer an interactive textbook format, Ximera Calculus 1-2 is the most comprehensive.

Calculus Made Easy is strongly recommended as the first resource for those who find the subject intimidating, but it is neither interactive nor comprehensive.

AP Calculus AB should correspond to Calculus 1A and 1B. AP Calculus BC should correspond to Calculus 1C. If you took these courses recently in high school, we recommend using Expii Calculus 1 to test yourself and see if you need more review. If you never took those courses or it's been a long time, we suggest diving straight into MIT Calculus 1A through 1C.

Prerequisites

• High School Math

Resources

Format	Resource	Use cases	Length
text	Calculus Made Easy (Silvanus P. Thompson)	learn	292 pages
interactive text	Ximera Mooculus Calculus 1	learn
interactive text	Ximera Mooculus Calculus 2	learn
course	MIT Calculus 1A: Differentiation	learn	130 hours
course	MIT Calculus 1B: Integration	learn	130 hours
course	MIT Calculus 1C: Coordinate Systems & Infinite Series	learn	130 hours
interactive text	Expii Calculus 1	practice review
forum	/r/learnmath	help

Needed by

• Core Math

Multivariable Calculus

The recommended resource here is MIT Multivariable Calculus along with the Strang textbook Calculus.

An alternative for those seeking a purely text-based approach is to follow the Ximera Calculus 3 interactive textbook.

Prerequisites

• Single-variable Calculus

Resources

Format	Resource	Use cases	Length
interactive text	Ximera Mooculus Calculus 3	learn
text	Calculus (Gilbert Strang)	learn
course	MIT Multivariable Calculus	learn	156 hours
course	Khan Academy Multivariable Calculus	practice review
forum	/r/learnmath	help

Needed by

• Probability
• Linear Algebra (Advanced track)

Linear Algebra

Those who are brand new to linear algebra and who only have a background in high school math or single-variable calculus should take the Beginner track. Note that the textbook by Boyd and Vandenberghe does not contain all the topics of a full course on linear algebra, so if you choose to learn linear algebra exclusively by textbook you may need to transition to another resource later, such as Jim Hefferson's textbook from the Advanced track. However, as not all of linear algebra is necessarily used in every course, a more pragmatic approach to this problem might be to attempt taking the course that requires linear algebra and seeing what topics you are actually missing for understanding the course content, and then selectively learning those topics as needed.

If your math background is already very strong (i.e. through multivariable calculus), or you have some experience in linear algebra, you may find the Beginner track too slow or easy. In this case you could consider the Advanced track, which consists of Gilbert Strang's materials (e.g., MIT Linear Algebra). However, Strang's textbook is not available for free and his course requires you have access to MATLAB. If you do not wish to buy Strang's textbook, you could try using Hefferson's free textbook. And it may be possible to use GNU Octave instead of MATLAB, but we have not tested this option.

Gilbert Strang's material on linear algebra is perhaps the very best on this topic, so if you are planning to study advanced topics in linear algebra, you may want to look at Advanced after Beginner.

If you have already studied linear algebra but it's been a long time, the Advanced track contains a review/reference text. Go through the text and confirm that you are familiar with everything on there. Whenever you find you have forgotten something, go through Strang's online course to find that material and review it.

Beginner track

Prerequisites

• High School Math

Resources

Format	Resource	Use cases	Length
video	Essence of Linear Algebra	prepare
course	UT Linear Algebra: Foundations to Frontiers	learn	120 hours
text	Applied Linear Algebra (Stephen Boyd and Lieven Vandenberghe)	learn	473 pages
forum	/r/learnmath	help

Advanced track

Prerequisites

• Multivariable Calculus
• MATLAB license

Resources

Format	Resource	Use cases	Length
course	MIT Linear Algebra	learn	130 hours
book	Introduction to Linear Algebra (Gilbert Strang)	learn	584 pages
book	Linear Algebra (Jim Hefferson)	learn	507 pages
text	"Linear Algebra Review and Reference"	review	26 pages
forum	/r/learnmath	help

Needed by

• Machine Learning
• Cryptography
• Graphics
• Robotics

Probability

The MIT Probability course is much more in-depth than one would need for much of computer science, but it would be critical for those who are going into data science.

Our discrete mathematics materials will also teach some probability, which may be sufficient for some computer science students; however, it might be necessary to supplement knowledge of discrete probability using some of the other resources here.

Prerequisites

• Multivariable Calculus

Resources

Format	Resource	Use cases	Length
text	Grinstead and Snell’s Introduction to Probability	learn	518 pages
course	MIT Introduction to Probability: The Science of Uncertainty	learn	216 hours
course	Khan Academy Statistics & Probability	practice review
forum	/r/learnmath	help

Needed by

• Core Distributed Systems
• Machine Learning (TODO)

Physics

The first course is a very popular introduction to physics that you can take to get you interested in the topic, but it is optional.

Prerequisites

• Single-variable calculus

Resources

Format	Resource	Use cases	Length
course	UVA How Things Work: An Introduction to Physics	prepare inspiration	17 hours
course	Rice Mechanics, Part 1	learn	36 hours
course	Rice Mechanics, Part 2	learn	36 hours
interactive text	Expii Mechanics	practice review
course	Rice Electricity and Magnetism, Part 1	learn	70 hours
course	Rice Electricity and Magnetism, Part 2	learn	70 hours
interactive text	Expii Electricity, Magnetism, Optics	practice review

Needed by

• Advanced Computing Systems