Build proof habits from concrete cases to general arguments across the discrete math tools CS students use most
4 sections · 9 lessons
Define truth tables, necessary and sufficient conditions, and quantifier order, then test exact wording against near-miss cases.
3 lessonsCompare set operations, function types, and equivalence relation properties, using symbols, diagrams, and matching definitions to meanings.
3 lessonsTrace paths in concrete graphs, then compute factorial patterns and Pascal rows to ground counting claims before broader proof work.
2 lessonsWrite base case and inductive step as labeled moves, verify small cases, and use a proof checklist to close recurrence arguments.
1 lessonPropositional logic starts the course with truth tables and visible cases, then moves into the language of proof: conditions, quantifiers, sets, functions, relations, graphs, counting, and induction. The course is built for CS and math students who want to read and write cleaner proofs, spot bad reasoning, and justify claims with precise examples before they generalize. By the end, the core discrete math objects are no longer just definitions, but usable proof tools.
Truth tables for propositional connectives, necessary and sufficient conditions, quantifier order, set operations, function types, equivalence relations, graph connectivity, factorial growth, Pascal’s triangle, and induction as a proof script. The course also touches proof-checking habits such as exact wording, labeled base cases, and inductive steps.
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Something to operate in every section.
Three findings from decades of learning research shaped how every Fenzo lesson is built.
Average pass rate · Freeman et al., PNAS 2014
What the science says
Students in lecture-only classes are 1.5× more likely to fail.
How Fenzo does it
Every Fenzo lesson is interactive. No passive reading or watching, ever.
You work through itAI does it for you
Skill retention over time · with vs. without practice
What the science says
Offloading thinking to AI erodes the very skills you’re trying to build.
How Fenzo does it
Fenzo makes you do the thinking — guided, but never done for you.
Retrieval practiceRe-reading
Long-term recall · retrieval vs. re-reading
What the science says
Recalling information beats re-reading it for building durable understanding.
How Fenzo does it
Lessons weave in quizzes and recall prompts, so it sticks.