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Research draft

sum

vr.tr.sum · XCT.QLT

Let an agent compute and explain sums, use summation notation and rules, evaluate series and Riemann sums, and support learning across levels.

Thing Registry Cross-cutting context

Research draft, second pass

A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.

written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify

Researched by: Claude

Purpose and description

Let an agent compute and explain sums, use summation notation and rules, evaluate series and Riemann sums, and support learning across levels.

The result of adding numbers, quantities or other addable objects together, from simple arithmetic sums and digit sums to partial sums of series, Riemann sums approximating integrals, sums of powers, weighted sums and the empty sum equal to zero; summation is notated with the sigma symbol and underlies arithmetic, algebra, analysis and statistics.

What it is for: Results of addition.

It can be compute sums; explain summation notation and rules; evaluate series and Riemann sums; support learning.

Distinguishing features

Additive

Finite or infinite

Notated with sigma

Foundational

What it looks like

Not physical; numbers and expressions with the sigma symbol.

How it is recognised

Result of adding

Sigma notation

A product is the result of multiplying

Related models

is a kind of - category

operation result

is a kind of - category

weighted sum

is related to - computing sums

calculation

is related to - divisor sums

amicable numbers

In practice

Families and kinds

finite arithmetic sums

digit sums and sums of powers

partial sums and series

Riemann sums

weighted sums and the empty sum

Standards and regulation

Mathematical notation conventions

Failure modes and hazards

Off-by-one errors in index ranges

Misusing divergent series

Floating point accumulation error

Also called

Riemann sumpartial sumPositive elementdigit sumSums of powersempty sumtelescoping sumaliquot sumdouble sumalgebraic sumexponential sumcharacter sumdebitDelta-v budgetsums of three cubessum of normally distributed random variablesgrowing-degree daysum of a seriessum of decimal digitsWeyl sumsKloosterman sumnet debit requiredBaskerville-Emin GDD

Where this came from

wikidata · CC0 1.0

Source repository Registry entry point

Also registered as vr.tr.sum-artifact

Drafted structure

Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.

Compute Working out sums.

Arithmetic.

Basic

Basic sums.

Basic

Basic sums.

  1. What is the sum of these numbers, and how can it be checked? action
  2. What is a digit sum, and how is it used in checks? definition

Formulas

Closed forms.

Formulas

Closed forms.

  1. Which closed-form formulas give sums of arithmetic and geometric progressions and sums of powers? definition
  2. How are they proved? definition
Notation Sigma notation.

Rules.

Sigma

Reading and writing sums.

Sigma

Sigma notation.

  1. How is sigma notation read and written, including index ranges and the empty sum? definition
  2. How are sums manipulated by linearity, reindexing and splitting? definition

Weighted

Weighted sums.

Weighted

Weighted sums.

  1. What are weighted sums, and how do averages, expectations and dot products use them? definition
  2. How is a weighted sum computed here? action
Analysis Series and integrals.

Advanced.

Series

Partial sums and series.

Series

Series.

  1. What are partial sums, and when does an infinite series converge? definition
  2. Which tests decide convergence? definition

Riemann

Riemann sums.

Riemann

Riemann sums.

  1. How do Riemann sums approximate integrals, and how does the approximation improve? definition
  2. How is a Riemann sum computed for this function? action
Learn Teaching and computing.

Education.

Teach

Teaching sums.

Teach

Teaching.

  1. How can summation be taught from arithmetic to sigma notation? action
  2. Which misconceptions arise? provenance

Numeric

Numerical summation.

Numeric

Numerical summation.

  1. How can floating point summation error be reduced, such as by compensated summation? action
  2. Which entry fits numerical methods? action

What the second pass must settle

  • Should series be a separate entry?
  • How should notation guides be linked?
  • How should numerical methods be linked?
Draft as JSON