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Mathematics for Computer Science

courses.csail.mit.edu

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Re: Mathematics for Computer Science

#11

Post by drostie »

joshzayin wrote: post #3

I find it somewhat strange that generating functions are introduced significantly before recurrences are (and that recurrences are introduced last!). Does anyone know why the authors did that?

I would guess that it's something like SICP introducing assignment halfway through the book, dramatic, unexpected, and you've been using a weaker version for many chapters now. (Chapter 6 is about recursive data types, and comes immediately after chapter 5's induction to give some perspective.) But it might also be because, as an introductory mathematics course, it wants to stay a good distance away from algorithms and messy concepts like big-O notation.

Re: Mathematics for Computer Science

#12

Post by spicyj »

joshzayin wrote: post #3

I find it somewhat strange that generating functions are introduced significantly before recurrences are (and that recurrences are introduced last!). Does anyone know why the authors did that?

Recurrences are partially covered in chapters:

  13 (Sums and Asymptotics)
  15 (Generating Functions, as you mentioned)
  19 (Random Processes)
  20 (Recurrences)
and though they're not explicitly named as such in Chapter 5 (Induction), several of the problems in the chapter make use of them.

It seems to me that the first half of the chapter on recurrences covers recurrences more from a CS viewpoint such as the recurrence they list for mergesort:

  T(n) = 2 T(n/2) + n - 1
which is arguably less fundamental than the study of linear recurrences which come up more often in math. The second half of the chapter covers techniques for solving general recurrences, both for general linear recurrences and general divide-and-conquer recurrences using the Akra-Bazzi theorem (which is an extension of the Master Theorem).

Thus, perhaps the chapter "Recurrences" is misnamed – the authors certainly cover elementary recurrences in the earlier chapters and leave more complex topics recurrences (such as how to solve them in general) for the end because they are less important than most of the other topics in the book.

Re: Mathematics for Computer Science

#13

Post by k3fernan »

Just a question for CS graduates here, how many Math courses were required to major in CS?

When I was an undergraduate the bare minimum was:

- 2 algebra (number theory + linear algebra)

- 2 calculus (single variable)

- 2 statistics

- 1 logic

- 1 combinatorics (graph theory + enumeration)

There was no "Math for CS" course per say, there was just math you should know. And that was the bare minimum for a BCS, the BMath (CS) had even more. I myself struggled with those courses (mostly the "raw" math courses rather the CS-y ones) but I'm grateful now that I did them. Math and Computer Science are so intrinsically linked.

Re: Mathematics for Computer Science

#15

Post by jc4p »

k3fernan wrote: post #13

Just a question for CS graduates here, how many Math courses were required to major in CS? When I was an undergraduate the bare minimum was: - 2 algebra (number theory + linear algebra) - 2 calculus (single variable) - 2 statistics - 1 logic - 1 combinatorics (graph theory + enumeration) There was no "Math for CS" course per say, there was just math you should know. And that was the bare minimum for a BCS, the BMath…

I'm probably going to be the sore one out when people from better schools start posting replies, but at my school which has a very small computer science department (so small that I'm not even doing the CS major even though I'm a professional) only requires:

- Calculus I

- Calculus II

- Introductory Statistics

Re: Mathematics for Computer Science

#16

Post by spicyj »

k3fernan wrote: post #13

Just a question for CS graduates here, how many Math courses were required to major in CS? When I was an undergraduate the bare minimum was: - 2 algebra (number theory + linear algebra) - 2 calculus (single variable) - 2 statistics - 1 logic - 1 combinatorics (graph theory + enumeration) There was no "Math for CS" course per say, there was just math you should know. And that was the bare minimum for a BCS, the BMath…

At Carnegie Mellon, the following are required:

  * elementary discrete math
  * intermediate discrete math / intro CS theory
  * calculus I
  * calculus II
  * linear algebra
  * probability
  * an "algorithms and complexity" elective:
    combinatorics, graph theory, automata, etc.
I might be missing one or two.

Re: Mathematics for Computer Science

#17

Post by r15habh »

k3fernan wrote: post #13

Just a question for CS graduates here, how many Math courses were required to major in CS? When I was an undergraduate the bare minimum was: - 2 algebra (number theory + linear algebra) - 2 calculus (single variable) - 2 statistics - 1 logic - 1 combinatorics (graph theory + enumeration) There was no "Math for CS" course per say, there was just math you should know. And that was the bare minimum for a BCS, the BMath…

I completed my graduation last year, the compulsory Math courses at my time were:

- Linear algebra

- Calculus (single variable)

- Discrete mathematics

- Probability & Statistics

- Numerical Methods & transforms

Re: Mathematics for Computer Science

#18

Post by strawbucks »

matlaber wrote: post #14

I took this class last semester! As a mechanical engineering major who is interesting in computer science I really enjoyed it (the Psets were a bit annoying sometimes though). The text is pretty easy to read too.

Was it TEAL last semester? That's really what made me dislike the class the most, as well as the less-than-helpful staff.

Re: Mathematics for Computer Science

#19

Post by joshzayin »

spicyj wrote: post #16
k3fernan wrote: post #13

Just a question for CS graduates here, how many Math courses were required to major in CS? When I was an undergraduate the bare minimum was: - 2 algebra (number theory + linear algebra) - 2 calculus (single variable) - 2 statistics - 1 logic - 1 combinatorics (graph theory + enumeration) There was no "Math for CS" course per say, there was just math you should know. And that was the bare minimum for a BCS, the BMath…

At Carnegie Mellon, the following are required: * elementary discrete math * intermediate discrete math / intro CS theory * calculus I * calculus II * linear algebra * probability * an "algorithms and complexity" elective: combinatorics, graph theory, automata, etc. I might be missing one or two.

This is assuming you don't count the algorithm design and analysis class as math, or any of the "logic and languages" (Intro PL, constructive logic, Automated program verification, basic logic, computability and incompleteness) as math.

Re: Mathematics for Computer Science

#20

Post by sakopov »

k3fernan wrote: post #13

Just a question for CS graduates here, how many Math courses were required to major in CS? When I was an undergraduate the bare minimum was: - 2 algebra (number theory + linear algebra) - 2 calculus (single variable) - 2 statistics - 1 logic - 1 combinatorics (graph theory + enumeration) There was no "Math for CS" course per say, there was just math you should know. And that was the bare minimum for a BCS, the BMath…

Here is what I remember taking for my CS degre at university of KC.

Trigonometry Calculus I Calculus II Calculus III Differential Equations Discrete Algebra I Discrete Algebra II Statistics Applied Probability and Network analysis Numerical Analysis Engineering Physics I Engineering Physics II Algoriths and datastructures

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