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A language of polynomials.

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A Language of Polynomials

Each slide can be formalized even further as their own research paper but presenting in this manner allows my ideas to give intuitive bearing so that it gives people from various backgrounds to come up with their own theories, ideas, and applications. On the other hand, this is also a formalized proof in my style of construction. A clean version can be found here.

1. Foundations

Foundations

2. Monomial of One Degree

Monomial of One Degree

3. Addition

Addition

4. Product

Product

5. Problem with Matrices

Problem with Matrices

6. Multivariable Polynomials

Multivariable Polynomials

7. Generalized Monomial Deciders

Generalized Monomial Deciders

8. Concentric Monomial Deciders

Concentric Monomial Deciders

9. Constants

Constants

10. Division

Division

11. Multiple Divisions

Multiple Divisions

12. Equivalence

Equivalence

13. Reversing

Reversing

14. Corollary of Reversing

Corollary of Reversing

15. Godel's Theorem

Godel's Theorem

16. Constructing The One Way Function

Constructing The One Way Function

17. Infiniteness

Infiniteness


References

Berstel, J., & Reutenauer, C. (2010). Noncommutative rational series with applications. Cambridge University Press.

Sipser, M. (2006). Theory of Computation (2nd ed., p. 431). Course Technology, Cengage Learning.

Munkres, J. R. (2000). Topology (2nd ed., p. 537). Prentice Hall.

Artin, M. (2011). Algebra (2nd ed., p. 543). Pearson.

Enderton, H. B. (2001). Logic (2nd ed., p. 317). HARCOURT/ACADEMIC PRESS.

Lay, S. R. (2004). Analysis (4th ed., p. 394). Pearson Prentice Hall.

Cox, D. A., Little, J., & O’Shea, D. (1997). Ideals, varieties, and algorithms: An introduction to computational algebraic geometry and commutative algebra (2nd ed.). Springer.

Golub, G. H., & Van Loan, C. F. (1996). Matrix Computations (3rd ed., p. 728). Johns Hopkins University Press.

Hofstadter, D. R. (1999). Gödel, Escher, Bach: An eternal golden braid. Basic Books.

Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2009). Introduction to Algorithms (3rd ed.). MIT Press.

Sturtivant, C. (n.d.). CS&E Profile: Carl Sturtivant. University of Minnesota. Retrieved November 30, 2023, from https://www-users.cse.umn.edu/~carl/.

Shilov, G. E. (2012). Linear algebra (R. A. Silverman, Trans.). Dover Publications. (Original work published 1971)

Strang, G. (2009). Introduction to Linear Algebra (4th ed., p. 585). Wellesley-Cambridge Press.

Rosen, K. H. (2006). Discrete Mathematics And Its Applications (6th ed.). McGraw-Hill Education.

Prasolov, V. V. (1995). Intuitive topology. American Mathematical Society.

Carter, N. (2009). Visual group theory. Mathematical Association of America.

Spivak, M. (2008). Calculus (4th ed., p. 680). Publish or Perish.

Sullivan, M. (2008). Precalculus (8th ed., p. 1152). Prentice Hall.

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A language of polynomials.

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