Ai_Engineering vs Calculus & Probability Lab

Become an AI engineer—starting exactly where you are. Ai_Engineering is a complete, interactive learning environment for iPhone, iPad, and Mac. It begins with computing, Python, and mathematical intuition, then builds toward language models, retrieval, agents, evaluation, multimodal systems, inference, safety, infrastructure, and principal-level architecture. LEARN BY DOING • 40 structured courses from beginner to advanced • 400 substantive interactive lessons • 140 editable, syntax-highlighted code labs • 100 quizzes with validation and explanations • 80 architecture decisions based on real trade-offs • 80 guided concept exercises • Progressive hints that help without giving the answer away BUILD A PORTFOLIO Complete 40 practical projects across beginner, intermediate, and advanced levels. Every build includes an editable workspace, milestones, local checks, and a clear outcome you can explain in an interview. YOUR PRIVATE AI TUTOR Ask questions from any lesson or project. Tutor Core explains ideas patiently from basic arithmetic upward, uses the current learning context, and can run offline. On compatible devices, Apple on-device intelligence adds private generative tutoring. Connecting an external provider is always optional. SEE YOUR AI TAKE SHAPE Every completed lesson, course component, and project milestone contributes to a living AI-construction visualization. Watch the neural system assemble as your skill grows. DESIGNED FOR SERIOUS PROGRESS Earn XP, build streaks, bookmark material, track skill readiness, choose daily goals, and move naturally between iPhone, iPad, and Mac. START FREE Download and begin without an account. The first module of every course is free, so you can experience the lessons, exercises, saved progress, and offline-first learning flow before deciding whether to upgrade. AI_ENGINEERING PRO Pro unlocks the complete 40-course curriculum, all 400 lessons and 140 code labs, all 40 portfolio projects, contextual Tutor Core, and the full progress experience across iPhone, iPad, and Mac. Choose Pro Monthly or Pro Annual. Eligible new subscribers can start with a 7-day free trial. The localized price and renewal period are shown before purchase. Payment is charged to your Apple Account when you confirm. The subscription renews automatically unless cancelled at least 24 hours before the end of the current period. You can restore purchases in the app and manage or cancel from Apple Account subscription settings. If a subscription expires or is cancelled, completed progress remains saved and the free tier remains available. Terms of Use (EULA): https://www.apple.com/legal/internet-services/itunes/dev/stdeula/ Privacy Policy: https://www.lukekevinmclaughlin.com/privacy

Calculus & Probability Lab turns two of the hardest STEM subjects into something you can see, touch, and drag with your finger. Instead of static graphs in a textbook, every derivative, integral, and probability distribution becomes a real 3D object you orbit, zoom, and reshape live. Whether you're in AP Calculus, a first-year college calculus or statistics course, or just relearning math you forgot, this app trades memorized formulas for visual intuition: drag a point along a curve and watch its tangent-line slope update instantly, or watch a histogram built from real dice tosses close in on the bell curve as you roll. FUNCTION LAB — 3D VISUALIZER • 22 function families: lines, parabolas, cubics, quartics, sine/cosine waves, exponentials, natural logs, reciprocals, square roots, Gaussian bumps, logistic S-curves • Genuine z = f(x, y) surfaces — paraboloids, saddles, Gaussian hills, ripples, sphere caps, cones, tilted planes, monkey saddles, egg-carton surfaces, twin peaks — drag to orbit, pinch to zoom • Live tangent-line overlay — move a point along any curve and watch the exact derivative f'(x) recompute in real time • Riemann sum overlay — slide from 1 to 60 rectangles and watch the sum converge to the exact definite integral • Every formula is closed-form and exact — no approximation, no drift PROBABILITY LAB — PHYSICS DICE • Toss physics-simulated dice and build a genuine empirical histogram, roll after roll • Scenarios span dice-sum outcomes, coin-flip binomial trials, and Poisson arrival processes • Overlay your empirical results against the exact theoretical distribution on the same chart • Watch the Central Limit Theorem happen live: enough trials and the histogram closes in on the normal curve • Track empirical mean against theoretical mean at every roll LEARNING PATH — 4 WORLDS, ~50 LESSONS • World 1, Functions & Limits: what a function is, families of functions, slope, one- and two-sided limits, continuity, average vs. instantaneous rate of change, exponentials and logs • World 2, Derivative Lab: the derivative as slope, power/product/quotient/chain rules, higher derivatives, tangent planes and partial derivatives, critical points, related rates, optimization, the Mean Value Theorem • World 3, Integral Lab: area under a curve, Riemann sums, the definite integral, antiderivatives, the Fundamental Theorem of Calculus, net change, average value, area between curves, volumes of revolution, improper and numerical integration • World 4, Probability & Distributions: sample space and events, combining probabilities, the two-dice sum, random variables, expected value, binomial and Poisson models, the normal curve • Every lesson deep-links straight into the matching 3D lab, so theory and visualization reinforce each other AI TUTOR • Tap Explain on any surface, formula, or dice distribution and get a plain-language breakdown of exactly what's in front of you — your specific coefficients, your specific slope, your specific mean and standard deviation, not a generic textbook definition BUILT FOR REAL STUDY, NOT JUST BROWSING • Progress tracking across every world and lesson, so you always know where you left off • A limited number of dice rolls each day on the free tier; upgrade to roll without limits, unlock every function family and 3D surface, every lesson, and the AI tutor • A clean, dark, distraction-free interface built for a late-night study session, not a cluttered graphing-calculator UI • Monthly and Annual plans, with a 3-day trial on Annual — cancel anytime in your account settings Calculus and probability are usually taught as two separate walls of formulas to memorize before an exam. Calculus & Probability Lab treats them as one connected, visual subject — build the intuition once, and the formulas stop needing to be memorized at all. Terms of Use https://www.apple.com/legal/internet-services/itunes/dev/stdeula/ Privacy Policy https://coddykit.com/terms/privacy-policy