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Wednesday, June 22, 2022

Math required and resources for Computer Science 1st year students

These are the Computer Science Math Classes required for most 1st year programs. 

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Just to dispel any notions, you can certainly become a good coder/programmer without needing these higher level of mathematics. But if you want to know what goes on under the hood and understand different algorithms, it is beneficial. 

If you are studying in a bootcamp, they probably won't focus on these unlike in an academic environment such as university or college. 

Generally, you can start off with precalculus and algebra and then move on at your own pace to get up to speed! 

I will be updating this post and adding another for upcoming years including Calculus 2 and Linear Algebra 2, Discrete Mathematics, Probability, etc.) But it is really important to have a strong base before expanding on your knowledge. Specifically, precalculus and trigonometry show up throughout your academic career. 

Precalculus (Prerequisite and review): 

Forty Days to Mastery of Precalculus

Paul's Notes

I strongly advise solving problems and working through them, in addition to watching the videos.

Make sure to focus on logarithm, polynomial, and exponential functions.  In addition, work on synthetic division and analytical geometry. Lastly, learn about sigma notation,  sequences/sums, and proof by induction. 

Download the formula sheet here

Set Theory:

(sometimes its a part of pre-calc)

This subject doesn't usually get covered in high school. It is a branch of math logic. If you took Digital Systems (CS Course), you might recall De'Morgan's law and Venn diagrams which happen to be used here as well! 

It's important to recall the symbols, some of them are used frequently in other fields of mathematics. Linear Algebra uses unions and intersections (for example). 

Trigonometry:

(sometimes its a part of pre-calc)

Make sure to cover the inverse functions as well such as arcsin, arctan, etc. in addition to their counterparts. In college, you will not be permitted to use a graphic calculator and you will not always have a unit circle around... try practicing your trig on a scientific calculator if possible. 

Khan Academy Section

Pauls Notes 

Download the formula sheet here (precalculus with the major trig identities)

Calculus 1:

You will be learning about limits, derivatives, and integrals. This course is strongly based on proofs (induction, contradiction, etc.) . 

This also expands upon trigonometry in some ways and introduces new trigonometric terms such as sinh. 

Paul's Notes

Khan Academy Section (mostly high school calculus)

Help with limits

Download the formula sheet here

Books:

  • Calculus Made Easy by Silvanus P. Thompson (focuses on derivatives a lot, less on limits)
  • Calculus by James Stewart 

Linear Algebra:

Matrix manipulations, lots of higher dimensional thinking, not proof based. I found this course more intuitive than Calculus. Linear dependence, vectors, matrices, determinants, etc. 

Videos:

My playlist

Kim Brehm's playlist (amazing)

Khan Academy Section (limited amount of content)

Other content:

Lecture Slides

Archived version of Paul's Notes (the original version has been taken offline)

Codecademy guide and course (has some practical/code connections)

Guide for solving linear equations and matrices

Books: 

  • Elementary Linear Algebra by Howard Anton 
  • Linear Algebra by Jim Hefferon

General Resources:

Refer to the textbook the course requires or recommends. If you cannot afford the book, occasionally they have pdf versions on the internet for free. 
In addition, you can look at these as well: https://openstax.org/subjects (Free peer-reviewed books). 

Kim Brehm has a whole bunch of useful math videos

Thank you for reading, please share the article and follow me on twitter for more resources and guides!

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