MF50: Algebra and number patterns

One important use of letters in algebra is to describe patterns in a quantitative and general way. We look at the `sequences' of square numbers and triangular numbers, and derive formulas for the nth terms. A table of differences shed light on these and other number patterns.

This video belongs to Wildberger's MathFoundations series, which sets out a coherent and logical framework for modern mathematics.

Category:

Science & Technology

Tags:

• Mathematics
• foundations
• Wildberger
• algebra
• patterns
• squares
• triangular
• numbers
• table
• of
• differences

[newtonparticle]

Does the table of differences have any relation to 'derivatives'?

[njwildberger]

Hi newtonparticle,

Yes, the difference operator is the discrete analog of a derivative, and there are many parallels between the two concepts. That is one reason why young people would do well learning about tables of differences.

Good question.

[newtonparticle]

Thanks for the reply :-)

Would you be able to produce a small video to better explain this please?

I have seen this before in the book "A Primer on Numerical Sequences", but so far have not been able to make a crystal clear connection on how these relate to deriving an equation from a sequence on numbers - based on the depth and values in the table.

[peterhi503]

Wildberger, your videos are uniformly excellent.

[QuantumMaths]

This is my favorite YouTube channel.