flagIllinois

Math

Discrete Mathematics

Master Discrete Mathematics

Watch discrete math videos, practice with problem-solving strategies

students image

Probability and combinations were impossible. The step-by-step videos made everything click. Went from D to B in six weeks.

Alex Patel

pug

Why Discrete Mathematics Students Choose StudyPug

The complete learning system to master Discrete Mathematics

Search with Photo

Search with Photo

Upload Discrete Math problems—AI searches and finds the right lesson teaching the concept

Expert Video Teaching

Expert Video Teaching

Certified teachers break down probability, sequences, matrices, and graph theory step-by-step

Unlimited Practice

Unlimited Practice

5,000+ teacher-created practice questions prepare you for Discrete Mathematics exams

How Illinois Students Use StudyPug

1

Select Grade Level
Select Grade Level

Choose your Illinois grade (K-12) and current math topics.

2

Get Unstuck
Get Unstuck

Upload homework problems or browse curriculum-aligned lessons.

3

Practice & Master
Practice & Master

Work through similar problems until concepts stick.

4

See Results
See Results

Track progress and watch grades improve week by week.

Discrete Mathematics Help: Master Concepts FastHelp

Print

ID

Standard

StudyPug Topic

CC.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems.

CC.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").

CC.HSS.CP.A.2

Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

CC.HSS.CP.A.3

Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

CC.HSS.CP.A.5

Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

CC.HSS.MD.A.1

Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

CC.HSS.MD.A.2

Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

CC.HSS.MD.A.3

Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.

CC.HSS.MD.B.7

Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

CC.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

CC.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

CC.HSF.IF.A.3

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

CC.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

CC.HSF.BF.A.2

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

CC.HSF.LE.A.2

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

CC.HSA.SSE.B.4

Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.

CC.HSN.VM.C.6

Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

CC.HSN.VM.C.9

Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

CC.HSN.VM.C.10

Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

CC.HSN.VM.C.11

Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.

CC.HSA.REI.C.8

Represent a system of linear equations as a single matrix equation in a vector variable.

CC.HSA.REI.C.9

Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

CC.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

CC.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

CC.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

CC.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

CC.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

CC.HSN.VM.A.1

Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.

CC.HSN.VM.A.2

Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

CC.HSN.VM.B.5

Multiply a vector by a scalar.
Complete Illinois Discrete Mathematics Coverage

Discrete Mathematics Lessons

84

Video Explanations

707

Practice Problems

790

Illinois Standards

100% Aligned

Why Illinois Discrete Mathematics Students Love StudyPug

SAT Math Preparation

SAT Math Preparation

Practice with real SAT-style discrete math questions—be ready for test day

Certified Teachers

Certified Teachers

Learn from expert Illinois teachers who know exactly what you need for Discrete Mathematics

Learn Anywhere

Learn Anywhere

Desktop, tablet, or phone—your Discrete Mathematics lessons sync across all devices

Get Started Today

Success Stories

Matrices and vectors were my weakness. The AI photo search found exact lessons instantly. Aced my final with a 94%.

Jordan Kim

Graph theory made no sense until StudyPug. The visual explanations finally made it click. Improved my grade from C+ to A-.

Taylor Rodriguez

Read More

Frequently Asked Questions

Get answers to common questions about learning Discrete Mathematics with StudyPug

What does Discrete Mathematics coverage include?

Complete Discrete Math curriculum with video lessons on probability, sequences, matrices, vectors, and graph theory. Includes practice problems, step-by-step solutions, and progress tracking for every topic.

How does the AI photo search work for discrete math problems?

Take a photo of any discrete math problem, and our AI finds the exact lesson teaching that concept. It's like having a personal tutor who knows exactly what you need for complex topics.

Are the teachers certified Illinois educators?

Yes! Our teachers are certified Illinois educators who understand Discrete Mathematics curriculum and create lessons specifically for Illinois standards and SAT preparation.

Can I use StudyPug on my phone or tablet for discrete math?

Absolutely! StudyPug works on desktop, tablet, and mobile. Your progress syncs automatically so you can study probability, sequences, and matrices anywhere.

How will StudyPug help me prepare for SAT Math?

We include SAT-style practice questions covering discrete math concepts like probability and sequences. Students report significantly improved scores and confidence on test day.

How StudyPug Works
Join Today

Practice Smart, See Real Progress

Unlimited Targeted Practice
Unlimited Targeted Practice

10,000+ questions adjust to your exact skill level. Never run out of problems that challenge you.

Visual Progress Tracking
Visual Progress Tracking

See mastery percentage for every topic. Parents get weekly progress emails automatically.

Achievement System
Achievement System

Earn badges for consistency and improvement. Build learning streaks that motivate daily practice

Detailed Analytics
Detailed Analytics

Time spent, problems solved, concepts mastered. Identify exactly where more practice is needed.

Start Now For Free
student
CallToActionContent

End Math Struggles Today

Illinois standard-aligned help that actually works

Start Now For Free
mathImage