Mathematical Expression and Reasoning - the course that teaches you to think like a computer scientist, not just code like one.
Logic, proofs, induction - I'll make the abstract concrete so you stop guessing and start reasoning.
✨ First Hour FREE!
CSC students expect to write code. CSC165 asks you to write proofs in formal mathematical language. Most students have never done this before - the whole mental model has to shift.
Mathematical induction is the #1 stumbling block. Students struggle with the structure: assuming P(k) to prove P(k+1) feels like assuming the thing you're proving. It is not - and once that clicks, everything opens up.
In CSC165, vague is wrong. "It is obvious that..." earns zero marks. Every step must be justified, every quantifier placed correctly, every logical gap explicitly closed. Examiners are ruthless about rigor.
An AI generated proof is the easiest thing in the world to submit without understanding. It looks rigorous, it uses all the right words, and you have no way to tell whether the inductive step actually closes. The exam will not accept that.
Code either runs or it does not, so a bad answer announces itself. A proof stays silent. AI writes confident, well formatted proofs with a quantifier in the wrong place or an inductive hypothesis that assumes the conclusion, and it reads fine until a grader takes it apart line by line.
Whether you can pick the right technique, state the hypothesis precisely, and justify every step in your own handwriting under time pressure. A proof you submitted but did not construct gives you zero practice at any of that.
Ask it to attack your proof instead of writing one. Ask for three more induction problems with the solutions withheld. Ask it to play the harshest grader in the department. You keep the speed and you build the skill the exam actually tests.
None of this makes you a bad student. It makes you a student learning to code in the AI era.
Every proof type has a skeleton. I give you the blueprint - the exact structure you fill in - so you're never staring at a blank page. Direct proof, contrapositive, contradiction, induction: each has a template.
We work through actual CSC165-style problems together. I annotate every step, flag every justification, and make the grader's expectations explicit - so your written proofs earn full marks.
CSC165 exams recycle patterns: induction on divisibility, predicate negation, bijection proofs. I know the recurring question types and drill you on them until the structure is automatic.
CSC165 is not abstract for its own sake. I connect proofs to algorithm correctness, Big-O reasoning, and the foundations of CSC236 and CSC263 so you understand why this matters beyond the course.
CSC165 is a prerequisite for nearly every upper-year CS course. Nail the foundations now - book a free first session.
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Not sure how much of a CSC165 proof you can construct with AI closed? Take the free AI Coding Dependency Test.
That is the most common CSC165 student profile. Programming ability does not transfer directly to proof writing. The good news: proof writing is a learnable skill with clear patterns. We will build yours.
First hour is FREE! After that:
Yes. One focused session on proof blueprints and induction structure can meaningfully move your marks. Message me now and we will build a crash plan for the exam topics.
Directly. CSC236 (Theory of Computation) builds on everything in CSC165 - induction, predicate logic, asymptotic notation. Solid CSC165 foundations make CSC236 significantly easier.
On the exam, yes, because the exam is handwritten and the technique has to come from you. But this is a very common place to be and it is fixable. Proof writing is pattern work: a handful of structures cover most of what CSC165 asks. Write one induction question with nothing open and see where you stall. If you want a broader read, the free AI Coding Dependency Test scores you across 10 skill areas in about 15 minutes.