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Question: why isn't linear algebra in here? I know this is a type of "but this isn't in my favorite list" question but since a lot of universities include it in

Question: why isn't linear algebra in here? I know this is a type of "but this isn't in my favorite list" question but since a lot of universities include it in their CS curriculum, I wonder why it isn't in here. Or did I oversee it? Is in there?

barronli 9y ago
I guess the book is more like “additional math for CS students beyond what a common CS curriculum has”.
- steaknsteak 9y ago
  Most of this stuff is part of common CS curriculums though. The real answer is just that you have to take linear algebra as a separate class. It's not supposed to be all the math for CS
throwaway080383 9y ago
Doesn't look like it. One might argue that linear algebra is slightly more niche than stuff like graph theoretic algorithms. There are applications to broadly useful things like gradient descent, but that seems to fall under numerical linear algebra which probably deserves its own course in the Applied Math department. N.b. just playing devil's advocate, I don't have a strong opinion either way.
- 323454 9y ago
  Then again, algebraic graph theory is key to understanding certain graph algorithms e.g. pagerank.
mjlee 9y ago
Because 6.042J is "an introduction to discrete mathematics, probability, and mathematical thinking for computer scientists". For linear algebra, see https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/ https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra... I'll admit I don't know how the MIT CS curriculum is structured, but I suppose it is in there, just not in this particular course.
- jmgrosen 9y ago
  This is actually the only math class that's required by the 6-3 degree program, MIT's CS degree. Many people do take linear algebra, though. Source: https://www.eecs.mit.edu/curriculum2016 https://www.eecs.mit.edu/curriculum2016 and I'm a 6-3
  - Vervious 9y ago
    A year or two ago the curricula still mandated one of 18.03 (diff equations) or 18.06 (linalg).
pharrington 9y ago
This is a discrete math course. edit: originally had posted, "This is a discrete math textbook."
joker3 9y ago
There are a few reasons. First, the purpose of a class like this is to prepare students for further coursework in algorithms and automata/complexity. You need logic, graphs and combinatorics for those a lot more than you need linear algebra. Second, the math department teaches a class in linear algebra. This is a collection of topics that you wouldn't ordinarily find in undergraduate math classes. Third, there's a limit on how much linear algebra you can cover in part of a course like this. Better to give it its own semester so you can treat the subject in some reasonable breadth.
- mlevental 9y ago
  i agree with you that this is in principle math for CS proper (rather than machine learning or numerical algos or something) but >Second, the math department teaches a class in linear algebra. This is a collection of topics that you wouldn't ordinarily find in undergraduate math classes. x math department doesn't have classes on graph theory, combinatorics, or prob & stats?
  - setr 9y ago
    At least in my school those were optional; only calc 1 & 2 and linear algebra were explicitly required, with combanatorics being commonly recommended but not required to grafuate
    - eftychis 9y ago
      Blows my mind at times when I talk to a math major in the U.S. with little to no knowledge of graph theory. Also the abstract algebra exposure seems to be kind of restricted -- for instance Math 120 at Stanford (Groups and Rings) is highly suggested but not required.
  - dsacco 9y ago
    You would not typically find dedicated undergraduate courses for graph theory, probability theory or combinatorics, no. At the very least you wouldn't expect to see those until you hit 300 level, but most likely not until graduate courses. Discrete mathematics is a grab bag of topics, and it's more fair to say that a discrete math course pulls in selected topics from other areas than to say it provides a focused coverage of any of them. At the depth each topic is taught, you couldn't pull it out into its own semester's worth of lectures. On the other hand, it would be very difficult to compact linear algebra into a discrete math course. Learning linear algebra already requires you to introduce a bunch of new concepts, like fields and vector spaces, linear equations, linear transformations, matrix representation and matrix operations, determinants, inner products... Equally importantly, linear algebra doesn't really "fit" with the topics of discrete mathematics, pedagogically speaking. It fits well with a treatment of multivariable calculus, but that's only a small part of what's taught in discrete math courses. If you wanted to teach linear algebra in a course covering a bunch of topics, you'd probably want to do a "topics in abstract algebra" course that works through groups, rings, modules, linear algebra and multilinear algebra. But then you're going well beyond what a non-math major should encounter in an undergraduate setting. Really, linear algebra stands on its own very well. In my opinion it should receive focused coverage and not be mixed with anything else. While graph theory and combinatorics can easily receive the same coverage, their treatment is usually pushed back to advanced undergraduate or graduate level courses because engineers don't usually work with them beyond what's covered in discrete math (which is exactly why we have discrete math as a standalone course). In fact, MIT actually lists linear algebra and multivariable calculus as prerequisites for the focused courses on combinatorics. The same applies for probability theory: you can't really learn probability theory (beyond discrete) without first learning analysis.
deleted 9y ago
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deanmen 9y ago
It's the textbook for a course calls "Mathematics for Computer Science" at MIT. Linear algebra is a separate course (18.06 or 18.700).

barronli 9y ago

I guess the book is more like “additional math for CS students beyond what a common CS curriculum has”.

steaknsteak 9y ago
Most of this stuff is part of common CS curriculums though. The real answer is just that you have to take linear algebra as a separate class. It's not supposed to be all the math for CS

throwaway080383 9y ago

Doesn't look like it. One might argue that linear algebra is slightly more niche than stuff like graph theoretic algorithms. There are applications to broadly useful things like gradient descent, but that seems to fall under numerical linear algebra which probably deserves its own course in the Applied Math department. N.b. just playing devil's advocate, I don't have a strong opinion either way.

323454 9y ago
Then again, algebraic graph theory is key to understanding certain graph algorithms e.g. pagerank.

mjlee 9y ago

Because 6.042J is "an introduction to discrete mathematics, probability, and mathematical thinking for computer scientists". For linear algebra, see https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/ https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra... I'll admit I don't know how the MIT CS curriculum is structured, but I suppose it is in there, just not in this particular course.

jmgrosen 9y ago
This is actually the only math class that's required by the 6-3 degree program, MIT's CS degree. Many people do take linear algebra, though. Source: https://www.eecs.mit.edu/curriculum2016 https://www.eecs.mit.edu/curriculum2016 and I'm a 6-3
- Vervious 9y ago
  A year or two ago the curricula still mandated one of 18.03 (diff equations) or 18.06 (linalg).

pharrington 9y ago

This is a discrete math course. edit: originally had posted, "This is a discrete math textbook."

joker3 9y ago

There are a few reasons. First, the purpose of a class like this is to prepare students for further coursework in algorithms and automata/complexity. You need logic, graphs and combinatorics for those a lot more than you need linear algebra. Second, the math department teaches a class in linear algebra. This is a collection of topics that you wouldn't ordinarily find in undergraduate math classes. Third, there's a limit on how much linear algebra you can cover in part of a course like this. Better to give it its own semester so you can treat the subject in some reasonable breadth.

mlevental 9y ago
i agree with you that this is in principle math for CS proper (rather than machine learning or numerical algos or something) but >Second, the math department teaches a class in linear algebra. This is a collection of topics that you wouldn't ordinarily find in undergraduate math classes. x math department doesn't have classes on graph theory, combinatorics, or prob & stats?
- setr 9y ago
  At least in my school those were optional; only calc 1 & 2 and linear algebra were explicitly required, with combanatorics being commonly recommended but not required to grafuate
  - eftychis 9y ago
    Blows my mind at times when I talk to a math major in the U.S. with little to no knowledge of graph theory. Also the abstract algebra exposure seems to be kind of restricted -- for instance Math 120 at Stanford (Groups and Rings) is highly suggested but not required.
- dsacco 9y ago
  You would not typically find dedicated undergraduate courses for graph theory, probability theory or combinatorics, no. At the very least you wouldn't expect to see those until you hit 300 level, but most likely not until graduate courses. Discrete mathematics is a grab bag of topics, and it's more fair to say that a discrete math course pulls in selected topics from other areas than to say it provides a focused coverage of any of them. At the depth each topic is taught, you couldn't pull it out into its own semester's worth of lectures. On the other hand, it would be very difficult to compact linear algebra into a discrete math course. Learning linear algebra already requires you to introduce a bunch of new concepts, like fields and vector spaces, linear equations, linear transformations, matrix representation and matrix operations, determinants, inner products... Equally importantly, linear algebra doesn't really "fit" with the topics of discrete mathematics, pedagogically speaking. It fits well with a treatment of multivariable calculus, but that's only a small part of what's taught in discrete math courses. If you wanted to teach linear algebra in a course covering a bunch of topics, you'd probably want to do a "topics in abstract algebra" course that works through groups, rings, modules, linear algebra and multilinear algebra. But then you're going well beyond what a non-math major should encounter in an undergraduate setting. Really, linear algebra stands on its own very well. In my opinion it should receive focused coverage and not be mixed with anything else. While graph theory and combinatorics can easily receive the same coverage, their treatment is usually pushed back to advanced undergraduate or graduate level courses because engineers don't usually work with them beyond what's covered in discrete math (which is exactly why we have discrete math as a standalone course). In fact, MIT actually lists linear algebra and multivariable calculus as prerequisites for the focused courses on combinatorics. The same applies for probability theory: you can't really learn probability theory (beyond discrete) without first learning analysis.

deleted 9y ago

[deleted]

deanmen 9y ago

It's the textbook for a course calls "Mathematics for Computer Science" at MIT. Linear algebra is a separate course (18.06 or 18.700).