The Mathematics Under Computer Science

# Build the mathematical footing the algorithms and ML tracks assume: rigorous sets and logic, the full linear-algebra arc, and a first real taste of topology.

# a suggested order, not a lock: jump anywhere, checkpoints track what you finish

1. Sets and Topology4 posts · 45 min

   Sets, logic and quantifiers, relations and functions, the algebra of sets: the grammar every proof is written in.

   1. What a Set Really Is: From Counting to the Foundations of MathematicsWant to Learn11 min scheduled
   2. Logic and Quantifiers: The Machinery That Makes Sets SpeakWant to Learn11 min scheduled
   3. Relations and Functions: The Architecture of Mathematical StructureWant to Learn12 min scheduled
   4. The Algebra of Sets: Operations, Laws, and Boolean StructureWant to Learn11 min scheduled
2. start here

   Linear Algebra11 posts · 2h 17m 1 self-checks

   The full linear-algebra arc, from vector spaces to the spectral theorem, closed by a synthesis post.

   1. The Geometry of Linearity: Why Vector Spaces MatterWant to Learn10 min
   2. Linear Transformations: The Language of ChangeWant to Learn11 min
   3. Matrices as Transformations: Rank, Span, and the Geometry of SolutionsDeep Dive12 min
   4. Change of Basis: Seeing Transformations Through New EyesDeep Dive12 min
   5. The Anatomy of Linear Maps: Injectivity, Surjectivity, and IsomorphismDeep Dive12 min
   6. Eigenvalues and Eigenvectors: The DNA of Linear TransformationsDeep Dive13 min scheduled
   7. Inner Product Spaces: Bringing Geometry into AlgebraDeep Dive12 min scheduled
   8. The Spectral Theorem: Symmetry, Structure, and OrthogonalityExpert14 min scheduled
   9. Orthogonal and Unitary Operators: The Geometry of Pure MotionExpert13 min scheduled
   10. Polar and Normal Operators: Decomposing Motion and MagnitudeExpert13 min scheduled
   11. A Complete Guide to Finite-Dimensional Linear Spaces: Linking the SeriesDeep Dive15 min scheduledquiz
3. Linear Algebra CapstoneDeep Dive5 minquiz

   Checkpoint: rank-nullity, eigenstructure, the spectral theorem and the SVD, in one adversarially checked quiz.

4. Linear Algebra10 mindemo

   optional

   Visualize transformations and eigenvectors as you read.

5. Sets and Topology6 posts · 1h 15m 1 self-checks optional

   Topology proper: open sets, continuity, connectedness, compactness, metric spaces, and building new spaces.

   1. What Is a Topology? Open Sets and the Shape of SpaceDeep Dive13 min scheduled
   2. Continuity and Homeomorphism: When Two Spaces Are the SameDeep Dive12 min scheduled
   3. Connectedness and Compactness: The Two Great Topological PropertiesDeep Dive13 min scheduled
   4. Metric Spaces: Where Distance Meets TopologyDeep Dive12 min scheduled
   5. Bases and Subbases: Building a Topology from BlocksDeep Dive12 min scheduled
   6. Building New Spaces: Products, Quotients, and Function SpacesExpert13 min scheduledquiz
6. Sets and Topology CapstoneExpert5 minquiz

   optional

   Optional capstone on sets and topology: Cantor, quantifier logic, the open-set axioms, continuity and compactness.

7. You have the math footing for the algorithms and ML tracks