Class prep · TJ Concrete Mathematics

Find the structure,then prove the result.

An independent course in discrete mathematics. Build proofs, work with sums and recurrences, and connect number theory, counting and finite probability through exact reasoning. Every problem has a full worked solution. Built by Neil Kothari, a TJ alumnus.

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$395 covers the full school year. The first lesson is free.

Try one. This is a test-level question from the course.

Problem 1

Test level
Multiple choice
No calculator
4 pts

In a finite universe $U$ , sets $P,Q$ satisfy both $P\cap Q=\varnothing$ and $P\cup Q=U$ . Which conclusion must hold?

original problems, each with a worked answer: 546; original problems, each with a worked answer
at test level or beyond: 378; at test level or beyond
short lessons, one for every topic: 42; short lessons, one for every topic
units, all open now: 7; units, all open now

Free lesson

Lesson 1.1: Statements, Sets and Quantifiers

Translate finite claims with clear domains, logical conditions and witness dependence.

Start with statements, sets and quantifiers. Track the domain and quantifier order, then use precise reasoning to decide what a claim establishes.

Problem 2

Core
True or false
No calculator
2 pts

Let $U=\{-2,0,3\}$ . Decide whether the following statement is true or false: for every $x\in U$ there is a $y\in U$ with $x+y=0$ . Justify your verdict using the stated universe.

Problem 3

Core
Multiple choice
No calculator
4 pts

Which statement is the exact negation of $\forall x\in\{1,2,3\}\;\exists y\in\{2,4\}:x<y$ ?

Open the rest of this lesson, free

The full lesson and all 13 of its problems, with every worked answer.

How it works

Class prep that works alongside class

A complete discrete mathematics course for students comfortable with precalculus algebra. Work alongside your school course or study the material in sequence. Each lesson starts with a concrete example, develops the idea, and shows how to check your reasoning before you try the practice.

Original problems in several formats: true or false, multiple choice, multi-part and free response.
Each one is marked core, test level or beyond.
Build direct proofs, test conjectures with valid counterexamples and justify each calculation with its assumptions.
A worked answer for every problem, ending with the mistake that most often costs points.
Proofs, finite sums, integer arithmetic, counting, generating functions, recurrences, finite probability and growth bounds.

What is inside

1Proofs and discrete reasoning6 lessons · 78 problems
2Finite sums and integer functions6 lessons · 78 problems
3Divisibility and congruences6 lessons · 78 problems
4Counting structures and identities6 lessons · 78 problems
5Sequences and recurrences6 lessons · 78 problems
6Formal generating functions6 lessons · 78 problems
7Finite probability and growth bounds6 lessons · 78 problems

The front entrance of Thomas Jefferson High School for Science and Technology

Who built it

Neil Kothari

TJHSST alumnus · Co-founder, EduAvenues · 10+ years in TJ preparation

Neil is a TJ alumnus and has spent more than a decade working with TJ students and their families. He built this course so students can connect discrete structures, exact calculations and mathematical proofs. Every problem is written for the course and every answer is checked before it goes in.

Tuition

$395for the full school year

One tuition covers every unit of the course. All 7 units are open now. The Statements, Sets and Quantifiers lesson stays free for everyone.

All 7 units: 42 lessons and 546 original problems
A worked answer for every problem
Access through the end of the school year

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