Discrete Math vs Quantum Physics

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/

Quantum Physics: Visual Lab is a beginner-friendly way to explore the strange and fascinating world of atoms, photons, electrons, and quantum behavior. Learn step by step with short lessons written in plain language. Build your understanding of wave-particle duality, the double-slit experiment, superposition, observation and measurement, entanglement, uncertainty, tunneling, qubits, photons, orbitals, quantum fields, and modern quantum technology. Open the Visual Lab to see abstract ideas in motion. Watch interference patterns form, compare particle and wave behavior, explore superposition, adjust uncertainty, observe tunneling probabilities, investigate entanglement, and visualize a qubit. Check your understanding with lesson-based quizzes and a daily quantum question. Review explanations after each answer, track your quiz accuracy, complete lessons, keep a study streak, and earn achievement badges as you progress. Use the glossary to look up key terms quickly, then visit the scientist timeline to learn about the people who shaped quantum physics, including Planck, Einstein, Bohr, Heisenberg, Schrodinger, Dirac, Feynman, and more. Features: - 18 beginner-focused quantum physics lessons - 7 interactive visual simulations - 110 quiz questions with explanations - Daily quantum question - Progress tracking, quiz accuracy, streaks, and achievements - Glossary of key quantum terms - Scientist timeline with short biographies - Plain-language examples, formulas, misconceptions, and real-world applications - Optional lifetime unlock to remove ads and open all premium content Quantum physics can feel mysterious, but it does not have to feel unreachable. Visual Lab turns difficult ideas into clear explanations and interactive moments you can explore at your own pace. Educational note: This app is designed for beginner learning and intentionally simplifies some advanced physics concepts.