Align math curriculum with CS2013

See: #637

README.md

@@ -190,32 +190,43 @@ Courses | Duration | Effort | Prerequisites
   - **Note**: probably the best resource to learn Haskell: [Haskell Programming from First Principles](http://haskellbook.com/) `paid`
 - **Required**, to learn about logic programming, backtracking, unification: [Learn Prolog Now!](http://lpn.swi-prolog.org/lpnpage.php?pageid=top)
 
-### Core math
-
-**Topics covered**:
-`linear transformations`
-`matrices`
-`vectors`
-`mathematical proofs`
-`number theory`
-`differential calculus`
-`integral calculus`
-`sequences and series`
-`discrete mathematics`
-`basic statistics`
-`O-notation`
-`graph theory`
-`vector calculus`
-`discrete probability`
-`and more`
+### Math Electives
+**Students must choose one of the following topics**: calculus, linear algebra, logic, or probability.
 
+#### Linear Algebra
 Courses | Duration | Effort | Prerequisites
 :-- | :--: | :--: | :--:
 [Essence of Linear Algebra](https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab) | - | - | pre-calculus
 [Linear Algebra - Foundations to Frontiers](https://www.edx.org/course/linear-algebra-foundations-to-frontiers-0) ([alt](http://ulaff.net/)) | 15 weeks | 8 hours/week | Essence of Linear Algebra
+
+#### Calculus
+Courses | Duration | Effort | Prerequisites
+:-- | :--: | :--: | :--:
 [Calculus 1A: Differentiation](https://www.edx.org/course/calculus-1a-differentiation) | 13 weeks | 6-10 hours/week | pre-calculus
 [Calculus 1B: Integration](https://www.edx.org/course/calculus-1b-integration) | 13 weeks | 5-10 hours/week | Calculus 1A
 [Calculus 1C: Coordinate Systems & Infinite Series](https://www.edx.org/course/calculus-1c-coordinate-systems-infinite-series) | 13 weeks | 5-10 hours/week | Calculus 1B
+
+#### Logic
+Courses | Duration | Effort | Prerequisites
+:-- | :--: | :--: | :--:
+[Introduction to Logic](https://www.coursera.org/learn/logic-introduction) | 10 weeks | 4-8 hours/week | set theory
+
+#### Probability
+Courses | Duration | Effort | Prerequisites
+:-- | :--: | :--: | :--:
+[Introduction to Probability - The Science of Uncertainty](https://www.edx.org/course/introduction-probability-science-mitx-6-041x-2) | 18 weeks | 12 hours/week | Multivariable Calculus
+
+### Math Core
+In addition to their math elective, students must complete the following course on discrete mathematics.
+
+**Topics covered**:
+`discrete mathematics`
+`mathematical proofs`
+`basic statistics`
+`O-notation`
+`discrete probability`
+`and more`
+
 [Mathematics for Computer Science](https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-spring-2015/index.htm)<sup>**1**</sup> | 13 weeks | 5 hours/week | Calculus 1C
 
 <sup>**1**</sup>: Students struggling with MIT Math for CS can consider taking the [Discrete Mathematics Specialization](https://www.coursera.org/specializations/discrete-mathematics) first.
@@ -324,21 +335,6 @@ Courses | Duration | Effort | Prerequisites
 [Introduction to Parallel Programming](https://classroom.udacity.com/courses/cs344) ([alt](https://www.youtube.com/playlist?list=PLGvfHSgImk4aweyWlhBXNF6XISY3um82_)) | 12 weeks | - | C, algorithms
 [Software Architecture & Design](https://www.udacity.com/course/software-architecture-design--ud821)| 8 weeks | 6 hours/week | software engineering in Java
 
-### Advanced math
-
-**Topics covered**:
-`parametric equations`
-`polar coordinate systems`
-`multivariable integrals`
-`multivariable differentials`
-`probability theory`
-`and more`
-
-Courses | Duration | Effort | Prerequisites
-:-- | :--: | :--: | :--:
-[Multivariable Calculus](https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/index.htm) | 13 weeks | 12 hours/week | MIT Calculus 1C
-[Introduction to Probability - The Science of Uncertainty](https://www.edx.org/course/introduction-probability-science-mitx-6-041x-2) | 18 weeks | 12 hours/week | Multivariable Calculus
-
 ### Advanced systems
 
 **Topics covered**:
@@ -394,7 +390,6 @@ If you are struggling, you can find a physics MOOC or utilize the materials from
 
 Courses | Duration | Effort | Prerequisites
 :-- | :--: | :--: | :--:
-[Introduction to Logic](https://www.coursera.org/learn/logic-introduction) | 10 weeks | 4-8 hours/week | set theory
 [Automata Theory](https://lagunita.stanford.edu/courses/course-v1:ComputerScience+Automata+SelfPaced/about) | 7 weeks | 10 hours/week | discrete mathematics, logic, algorithms
 [Computational Geometry](https://www.edx.org/course/computational-geometry-tsinghuax-70240183x) | 16 weeks | 8 hours/week | algorithms, C++
 [Introduction to Formal Concept Analysis](https://www.coursera.org/learn/formal-concept-analysis) | 6 weeks | 4-6 hours/week | logic, probability

extras/courses.md

@@ -33,6 +33,7 @@ Courses | Duration | Effort
 [Introduction to Mathematical Thinking](https://www.coursera.org/learn/mathematical-thinking) | 10 weeks | 10 hours/week
 [Introduction to Probability and Data](https://www.coursera.org/learn/probability-intro)| - | -
 [Linear Algebra (Strang)](https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/index.htm) | - | -
+[Multivariable Calculus](https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/index.htm) | 13 weeks | 12 hours/week
 
 ## Systems