What should be included in a freshman 'Mathematics for computer programmers' course?

Abstraction: Recommended math topics ranked by usefulness-to-difficulty for CS freshmen

Key points:

• Prioritized list (roughly by usefulness/difficulty ratio): general skills (fractions, logs, induction), asymptotics (Big-O), graph theory, linear algebra, combinatorics, probability, calculus, number theory, differential equations, information theory
• Graph theory flagged as "very hot topic in CS" likely for decades, especially combined with probability (e.g., social network algorithms)
• Domain-specific emphasis varies: financial programmers need probability, game programmers need linear algebra, cryptographers need number theory/information theory
• Author argues CS is a subfield of mathematics and laments universities offering CS without any math courses
• Generating functions noted as very useful but likely out of scope for a single course

Connections: Discrete Mathematics · Algorithms · Mathematics For Cs

Source: http://matheducators.stackexchange.com/questions/1734/what-should-be-included-in-a-freshman-mathematics-for-computer-programmers-cou/1745#1745