Excel: Vectorized Dynamic Modeling
Transform static worksheets into high-performance analytical engines using modern dynamic arrays and functional formula patterns. Learn to eliminate brittle grid dependencies, build recursive logic without VBA, and optimize the workbook calculation tree.
Like Duolingo, but for Excel: Vectorized Dynamic Modeling. Tomo turns the whole topic into a game you play five minutes a day, until it actually sticks.
A short one: 11 levels across 2 sections, about 22 minutes end to end, roughly 4 days at five minutes a day. It moves through Vectorizing the Calculation Grid and Functional Logic and Engine Tuning.
Free forever · No credit card · iPhone & Android
Key ideas in Excel: Vectorized Dynamic Modeling
- Appending the spilled range operator (#) to the top-left anchor cell (e.g., D2#) dynamically adapts to the entire spilled footprint as upstream data expands or contracts
- Hardcoding range endpoints like D2:D15 breaks automatic propagation and requires manual formula updates when upstream results grow
- The hash operator must follow a specific cell reference representing the origin anchor, not an entire column letter
- Excel logical functions like AND and OR aggregate their inputs into a single scalar TRUE or FALSE rather than returning an array of results
- Multiplication (*) acts as element-wise vectorized AND, while addition (+) acts as element-wise vectorized OR by coercing boolean arrays to 1s and 0s
- Modern Excel's calculation engine defaults to dynamic broadcasting, eliminating the need for legacy Ctrl+Shift+Enter (CSE) array entry
- The '@' symbol explicitly instructs the calculation engine to use implicit intersection, restricting calculation to the intersecting row or column instead of spilling
- Legacy Excel formulas opened in dynamic Excel without modification are automatically prefixed with '@' to prevent unexpected formula spilling
- Excel does not support nested arrays (arrays of arrays); passing an array into an aggregating or text-joining function that itself expects scalar or range inputs either reduces the entire range to one value or triggers a #CALC! nested array error
- Helper functions like BYROW and MAP iterate over multi-row arrays row-by-row using LAMBDA to deliver a spilled vector without nesting arrays
- Standard arithmetic operations (+, -, *, /) naturally broadcast across matching array dimensions without requiring row-by-row iterator projection
- CHOOSECOLS allows passing an arbitrary vector of column indices (e.g., 1, 10, 3) to extract and reorder columns simultaneously in memory
- Source tables remain untouched while generating an updated virtual layout that downstream functions can consume directly
- Negative integers in CHOOSECOLS count from the right, but explicit positive index lists yield precise multi-column reordering
- TOCOL and TOROW flatten 2D arrays into a 1D vector, using the scan_by_column boolean argument (default FALSE reads left-to-right, top-to-bottom)
- WRAPROWS folds a 1D vector into a 2D grid by filling each row up to wrap_count before moving to the next row
You've tried the other tabs
Thirty open tabs. Four facts you actually kept.
You watched. You nodded. By Sunday it was gone.
One answer, then back to scrolling.
Eight weeks. You meant to finish. You didn't.
Tomo gives Excel: Vectorized Dynamic Modeling the Duolingo treatment: levels, streaks, and quick quizzes that test what you just learned. That game loop is what the tabs above never had, so it's the one you actually finish.
Here's what playing it feels like
A real question from this course. Take your best guess.
Your array spilled down to D15. Why should you avoid pointing downstream formulas at D2:D15?
Get it right to open this lesson and 10 more in the app.
How to learn Excel: Vectorized Dynamic Modeling, step by step
Go in order. 11 short levels across 2 sections, about 22 minutes in all, five minutes a day.
- 1
Vectorizing the Calculation Grid
- Migrating from Cell Formulas to Spilled Arrays
- Reshaping Multi-Dimensional Data in Memory
- 2
Functional Logic and Engine Tuning
- Iterative State and Recursion with LAMBDA
- Dependency Tree and Memory Optimization
2 sections · 4 units · 11 levels. Built to play, not to enroll.
Questions about Excel: Vectorized Dynamic Modeling
How do I learn Excel: Vectorized Dynamic Modeling?
Go in order: start with Vectorizing the Calculation Grid, then Functional Logic and Engine Tuning. On Tomo that's 11 short levels, about 22 minutes in all, played five minutes a day. Start free and play the first level in under a minute.
Is there a Duolingo-style app for Excel: Vectorized Dynamic Modeling?
Yes. Tomo works like Duolingo: short daily lessons, streaks and quick quizzes. Excel: Vectorized Dynamic Modeling is one of its free courses, and you can type any other topic to get a course of your own.
Is the Excel: Vectorized Dynamic Modeling course free?
Yes. Excel: Vectorized Dynamic Modeling is playable on Tomo's free plan, which doesn't expire. No credit card, no waitlist. Download the app and start your first lesson.
How long does it take to learn Excel: Vectorized Dynamic Modeling?
11 levels across 2 sections, about 22 minutes of play in total. It's built for five minutes a day, so you finish it a little at a time instead of all at once.
Do I need any background to start Excel: Vectorized Dynamic Modeling?
No. It's pitched at an advanced level, so it starts where you are and builds up. If you can tap a phone, you can start.
Tomo is in ChatGPT
Tomo is also a ChatGPT plugin: the same playable courses, built and played inside your chat.
Add Tomo to ChatGPT- What to ask
- “Make me a Tomo course on black holes.” “Turn this chat into a Tomo course.”
- What you get
- Quick questions with instant feedback, hearts and stars, ready to play in about a minute.
- Where it goes
- No sign-up to start. Connect your Tomo account and your streak carries on in the app.
You pick the voice
Excel: Vectorized Dynamic Modeling is taught in the Pirate style: arr, learning be an adventure!. Want a different feel? In the app you can spin up the same topic in any of Tomo's teaching styles. Same facts, totally different vibe.
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