Discrete Mathematics curriculum

Start with 6.042J Mathematics for Computer Science and OpenDSA eTextbooks. Take notes until you can explain: Use propositions, predicates, quantifiers, implications, equivalence, and inference rules.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Formalize ten claims, test validity with truth tables or inference rules, and repair every ambiguous statement.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Translate precise claims between symbols and ordinary language.

Start with 6.042J Mathematics for Computer Science and OpenDSA eTextbooks. Take notes until you can explain: Write direct, contrapositive, contradiction, existence, uniqueness, and counterexample arguments.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Complete one proof by each major method and annotate the logical hinge in every argument.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Separate examples from proofs.

Start with 6.042J Mathematics for Computer Science and OpenDSA eTextbooks. Take notes until you can explain: Use set operations, Cartesian products, functions, injections, surjections, and bijections.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Classify functions and relations from definitions, then prove two classifications from first principles.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Analyze equivalence and partial-order relations.

Start with 6.042J Mathematics for Computer Science and OpenDSA eTextbooks. Take notes until you can explain: Use weak and strong induction.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Prove a summation or divisibility claim by induction and trace a recursive definition on a small input.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Define recursive structures and verify recursive algorithms.

Start with 6.042J Mathematics for Computer Science and OpenDSA eTextbooks. Take notes until you can explain: Use divisibility, gcd, Euclidean algorithm, congruence, primes, and modular inverses.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Solve a modular arithmetic set and explain one cryptographic or hashing application.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Apply modular reasoning to computation and cryptography.

Start with 6.042J Mathematics for Computer Science and OpenDSA eTextbooks. Take notes until you can explain: Use sum, product, permutation, combination, pigeonhole, inclusion-exclusion, and bijective counting.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Build a counting-method decision tree and solve mixed problems without double-counting.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Choose counting methods from structure.

Start with 6.042J Mathematics for Computer Science and OpenDSA eTextbooks. Take notes until you can explain: Use paths, connectivity, coloring, trees, spanning trees, directed graphs, and state machines.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Model a routing, scheduling, or dependency problem as a graph and justify the chosen algorithm.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Model networks and algorithms with graph structure.

Start with 6.042J Mathematics for Computer Science and OpenDSA eTextbooks. Take notes until you can explain: Solve basic recurrences and use asymptotic reasoning.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Analyze one recursive algorithm and one randomized process with recurrence, expectation, and explicit assumptions.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Use conditional probability, independence, expectation, and random variables in discrete settings.