Polynomials and Sequence Spaces - Wild Linear Algebra - NJ Wildberger

Polynomials and Sequence Spaces - Wild Linear Algebra - NJ Wildberger

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polynomials and sequence spaces; remark about expressions versus objects @ ;

2 of 26

2 of 26

polynomials and sequence spaces; remark about expressions versus objects @ ;

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Polynomials and Sequence Spaces - Wild Linear Algebra - NJ Wildberger

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  1. 1 CONTENT SUMMARY: pg 1: @
  2. 2 polynomials and sequence spaces; remark about expressions versus objects @ ;
  3. 3 pg 2: @ Some polynomials and associated sequences; Ordinary powers; Factorial powers D. Knuth;
  4. 4 pg 3: @10:34 Lowering factorial power; Raising factorial power; connection between raising and lowering; all polynomials @;
  5. 5 pg 4: @ Why we want these raising and lowering factorial powers; general sequences; On-line encyclopedia of integer sequences N.Sloane; 'square pyramidal numbers'; Table of forward differences;
  6. 6 pg 5: @19:23 Forward and backward differences; forward/backward difference operators on polynomials; examples: operator on 1 @;
  7. 7 pg 6: @ Forward and backward differences on a sequence; difference below/above convention;
  8. 8 pg 7: @27:21 Forward and backward Differences of lowering powers; calculus reference @;
  9. 9 pg 8: @31:27 Forward and backward Differences of raising powers; operators act like derivative @ ; n equals 0 raising and lowering defined;
  10. 10 pg 9: @ Introduction of some new basis; standard/power basis, lowering power basis, raising power basis; proven to be bases;
  11. 11 pg 10: @ WLA22_pg10_Theorem Newton; proof;
  12. 12 pg 10b: @44:40 Lesson: it helps to start at n=0; example square pyramidal numbers;an important formula @;
  13. 13 pg 11: @50:00 formula of Archimedes; taking forward distances compared to summation @
  14. 14 pg 12: @ a simpler formula; example: sum of cubes;
  15. 15 pg 13: @ exercises 22.1-4;
  16. 16 pg 14: @59:06 exercise 22.5; find the next term; closing remarks @;
  17. 17 Introduction
  18. 18 Some polynomials and associated sequences
  19. 19 Lowering factorial powers
  20. 20 Forward and backward differences
  21. 21 Differences of lowering and raising powers are easy to compute!
  22. 22 Factorial power bases
  23. 23 A theorem of Newton
  24. 24 A formula of Archimedes
  25. 25 A formula for sum of cubes
  26. 26 Exercises 22.1-4;

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