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In professional programming, most of the time, system design is most crucial and would use less of these mathematics. These 900 pages is not insurmountable. A d

by crphang 10y ago

In professional programming, most of the time, system design is most crucial and would use less of these mathematics. These 900 pages is not insurmountable. A discrete mathematics course for year 1 computer science students would have covered a good 70% of it. Such a course takes only 3 months and is 1/5 of a student's workload. The benefits of these is hardly questionable. Its use is apparent when you take a Design and Analysis of algorithms course like https://www.youtube.com/watch?v=JPyuH4qXLZ0 https://www.youtube.com/watch?v=JPyuH4qXLZ0. A good example of using knowledge of the pdf is analysing expected runtime of a hashtable. Which turns out to be theta(1) average case. Good analysis of algorithms inspire better design of it in general. Data structure and software engineering courses would probably be sufficient for many software engineering jobs out there. Databases, networks, OS and security are good to have knowledge. However, if an engineer is building cutting edge stuff, Mathematics will be his/her best friend. One good property of Mathematics is that it provide guarantees in the form of equality, inequalities or equivalences. Such guarantees can help you ensure that your system holds quantitatively. It is thus your job to reduce your computer science/engineering problem to a mathematics problem. I find this remark by Terence Tao particularly good: "If you don’t have mathematical background, the classes you take will help you train to analyze existing systems and build things that haven’t been built before. If you want to design something really new, at some point you’ll have to model what you’re doing, which might be different from previous models, and you have to do some mathematics somewhere." This remark is made in this interview: https://docs.google.com/document/d/1rinL25rC8LnMTzZcGjg1axT-0r-oiCnoKKH1DLQlmVA/edit https://docs.google.com/document/d/1rinL25rC8LnMTzZcGjg1axT-...

data4science 10y ago
Yes, mathematics has been, is, and will be at the cutting edge of software engineering. For historical examples: consider Turing, Knuth, and Page & Brin. For current examples: consider High Performance Computing (HPC), Data Science, and Data Engineering. For future examples: wait and see (or study math in the present). Also, consider etymology: computers are machines that preform computations; software is code that directs computations and their results on computers; software engineers create code that directs computations on computers; computational scientists define the limits of computing on computers that have given properties, and create novel computational solutions to problems; mathematicians discover the theory that computational scientists (and, more generally, all scientists) utilize. Note_0: There is a field at the cutting edge of computation, computational science, that requires the most mathematical knowledge of any discipline that includes the compute stem. Note_1: Math goes beyond providing guarantees of equality, inequality, and equivalence: it is the quantitative basis of computer science (and all science); it provides Boolean logic; it guarantees boundaries/possibilities; and it provides scope.
snmartin 10y ago
This is, in fact, a textbook for a discrete mathematics course for year 1 computer science students :)

by crphang 10y ago

data4science 10y ago

Yes, mathematics has been, is, and will be at the cutting edge of software engineering. For historical examples: consider Turing, Knuth, and Page & Brin. For current examples: consider High Performance Computing (HPC), Data Science, and Data Engineering. For future examples: wait and see (or study math in the present). Also, consider etymology: computers are machines that preform computations; software is code that directs computations and their results on computers; software engineers create code that directs computations on computers; computational scientists define the limits of computing on computers that have given properties, and create novel computational solutions to problems; mathematicians discover the theory that computational scientists (and, more generally, all scientists) utilize. Note_0: There is a field at the cutting edge of computation, computational science, that requires the most mathematical knowledge of any discipline that includes the compute stem. Note_1: Math goes beyond providing guarantees of equality, inequality, and equivalence: it is the quantitative basis of computer science (and all science); it provides Boolean logic; it guarantees boundaries/possibilities; and it provides scope.

snmartin 10y ago

This is, in fact, a textbook for a discrete mathematics course for year 1 computer science students :)