LLM Primer

Summary and Revision Notes

Use these notes to review Chapter 1 quickly.

Core Ideas

IdeaMeaningCheck yourself
notationcompressed languageCan you expand it into words?
variablename for a quantityCan you say what value or object it names?
expressionrecipe for computing a valueCan you substitute a small input?
functionreusable input-output ruleCan you identify input, rule, and output?
setcollection of distinct objectsCan you test membership?
tupleordered collectionCan you explain why order matters?
indexposition selectorCan you tell whether indexing starts at 0 or 1?
summationrepeated additionCan you expand it for three terms?
productrepeated multiplicationCan you expand it for three terms?

Key Notation

NotationRead asMeaning
xxxa named quantity
f(x)f(x)f of xthe output of function ff at input xx
a∈Aa \in Aa is in Amembership in a set
xix_ix sub ithe i-th item of xx
∑i=1nxi\sum_{i=1}^{n} x_isum from i equals 1 to n of x sub iadd the items
∏i=1nxi\prod_{i=1}^{n} x_iproduct from i equals 1 to n of x sub imultiply the items

Common Mistakes

  1. Reading f(x)f(x) as multiplication.
  2. Forgetting that mathematical indexing often starts at 1.
  3. Treating a set as ordered.
  4. Treating a tuple as unordered.
  5. Memorizing symbol names without reading what the symbols do.
  6. Moving past a formula before saying it in words.

Small Tests

Try these without looking back:

  1. If f(x)=x+2f(x) = x + 2, what is f(5)f(5)?
  2. If A={2,4,6}A = \{2, 4, 6\}, is 4∈A4 \in A?
  3. If x=(8,9,10)x = (8, 9, 10), what is x2x_2 in mathematical indexing?
  4. Expand ∑i=13ai\sum_{i=1}^{3} a_i.
  5. Say 1n∑i=1nℓi\frac{1}{n}\sum_{i=1}^{n}\ell_i in words.

If these feel unclear, return to the matching topic page. Do not rush into vectors while the notation still feels opaque.

If You Feel Lost

Return to a small example.

For a formula with a sum, use three values. For a function, plug in one number. For a set, write three members. The small case reveals the idea.

Bridge to Vectors

Vectors use this chapter immediately.

When you see

v=[v1,v2]v = [v_1, v_2]

read it as:

v is an ordered pair
v_1 is the first coordinate
v_2 is the second coordinate

That is enough to begin.