Linear Algebra World vs Discrete Math

Linear Algebra World (LAW) presents linear algebra in a way that is accessible yet rigorous. It is designed for students of engineering, mathematics, data science and related fields, and may also serve as a visual presentation tool for instructors. The app combines three roles: • matrix calculator • interactive algorithm step visualizer • carefully designed learning pathway through linear algebra Our goal is to present linear algebra as a coherent system built on a small set of axioms. Definitions are separated from consequences, logical dependencies are made explicit, and notation is kept minimal to reduce cognitive load. Visual tools are used extensively—even for abstract topics such as the four fundamental subspaces—so that geometric intuition and algebraic reasoning reinforce one another. The curriculum begins with vectors as coordinates and matrices as collections of vectors, and currently covers topics through QR factorization. Upcoming additions include OLS, eigendecomposition, SVD, and PCA. This app builds on our earlier Matrix Solver Step by Step, a highly rated matrix computation app used by students for several years. LAW adds a structured curriculum along with LaTeX import and export. LAW is designed for serious learners who want to understand the structure behind the computations. For quick step-by-step matrix calculations, Matrix Solver Step by Step may be the more direct tool. Your constructive feedback is essential to the continued refinement of the app.

Discretica helps CS students learn discrete math with interactive calculators, proof practice, and 500+ guided problems you can study offline. Built for Discrete Structures and Discrete Mathematics courses, Discretica focuses on the topics that show up in homework, quizzes, midterms, and finals. What you can study: - Logic and propositions: connectives, truth tables, equivalences, and quantifiers - Proof methods: direct proof, contradiction, contrapositive, and induction - Sets, functions, and relations: set operations, Venn diagrams, properties, and mappings - Counting and combinatorics: permutations, combinations, pigeonhole, and binomial theorem - Graph theory and trees: paths, cycles, connectivity, BFS, DFS, and spanning trees - Boolean algebra: expressions, laws, logic gates, simplification, and circuits - Number theory: divisibility, primes, modular arithmetic, GCD, LCM, and Euclidean algorithm Interactive tools: - Truth Table Builder for logical expressions with AND, OR, NOT, implication, biconditional, and XOR - Set Operations with union, intersection, difference, symmetric difference, cardinality, power sets, and Venn visuals - Combinatorics Calculator for permutations, combinations, factorials, and stars-and-bars - Modular Arithmetic for addition, subtraction, multiplication, powers, and inverses - Base Converter for binary, octal, decimal, and hexadecimal - GCD and LCM Calculator with Euclidean and extended Euclidean steps - Proof Trainer with fill-in-the-gap, reorder-the-proof, and choose-the-method exercises Practice that actually helps: - 500+ bundled practice problems across beginner, intermediate, and advanced levels - Hints, explanations, and step-by-step solutions - 30 rotating daily challenge problems - Mistake notebook with spaced review - Progress tracking with streaks, levels, topic mastery, and achievements - 54 formula and reference cards across the core syllabus Free to start: Use four free calculators, read the first subtopic in every module, complete daily challenges, and practice up to 8 problems per day. Discretica Premium unlocks all lessons, all tools, unlimited practice, step-by-step solutions, the full mistake notebook, and the proof trainer. Choose a weekly or yearly subscription, or unlock lifetime access with a one-time purchase. No account needed. No ads. Your learning progress, preferences, and mistakes are stored on your device. Terms of Use: https://www.apple.com/legal/internet-services/itunes/dev/stdeula/