Proof of the theorem

This book is for people who want to get acquainted with the concepts of basic geometry without taking a formal course. It can serve as a supplemental text in a classroom, tutored, or home-schooling environment. It should also be useful for career changers who need to refresh their knowledge of the subject. I recommend that you start at the beginning of this book and go straight through. This is not a rigorous course in theoretical geometry. Such a course defines postulates (or axioms) and provides deductive proofs of statements called theorems by applying mathematical logic.

322p zizaybay1103 29-05-2024 3 2   Download

This book is for people who want to get acquainted with the concepts of basic trigonometry without taking a formal course. It can serve as a supple- mental text in a classroom, tutored, or home-schooling environment. It should also be useful for career changers who need to refresh their knowledge of the subject. This is not a rigorous course in theoretical trigonometry. Such a course defines postulates (or axioms) and provides deductive proofs of statements called theorems by applying mathematical logic. Proofs are generally omitted in this book for the sake of simplicity and clarity.

322p zizaybay1103 29-05-2024 3 1   Download

The book treats three major areas: first (Chapters 3, 7, and 8), an analysis of channel models and the proof of coding theorems (theorems whose physical interpretation is that it is possible to transmit information reliably through a noisy channel at any rate below channel capacity, but not at a rate above capacity); second, the study of specific coding systems (Chapters 2, 4, and 5); finally, the study of the statistical properties of information sources (Chapter 6).

345p haojiubujain08 01-11-2023 2 1   Download

Continued part 1, part 2 of ebook "Understanding machine learning: From theory to algorithms" provides readers with contents including: additional learning models; advanced theory; dimensionality reduction; generative models; feature selection and generation; rademacher complexities; proof of the fundamental theorem of learning theory; multiclass learnability; compression bounds;...

165p tieulangtran 28-09-2023 8 4   Download

Part 1 of ebook "Proofs from the book" provides readers with contents including: number theory; geometry; six proofs of the infinity of primes; bertrand’s postulate; binomial coefficients are (almost) never powers; representing numbers as sums of two squares; the law of quadratic reciprocity; every finite division ring is a field; hilbert’s third problem - decomposing polyhedra; lines in the plane and decompositions of graphs; the slope problem;...

126p hanlinhchi 29-08-2023 6 2   Download

Continued part 1, part 2 of ebook "Proofs from the book" provides readers with contents including: analysis; combinatorics; graph theory; sets, functions, and the continuum hypothesis; in praise of inequalities; the fundamental theorem of algebra; pigeon-hole and double counting; tiling rectangles; identities versus bijections; five-coloring plane graphs; probability makes counting (sometimes) easy;...

188p hanlinhchi 29-08-2023 6 3   Download

Ebook "Graph theory with applications" is intended as an introduction to graph theory. Our aim has been to present what we consider to be the basic material, together with a wide variety of applications, both to other branches of mathematics and to real-world problems. Included are simple new proofs of theorems of Brooks, Chvátal, Tutte and Vizing. The applications have been carefully selected, and are treated in some depth. We have chosen to omit all so-called 'applications' that employ just the language of graphs and no theory.

270p tichhythan 17-08-2023 7 4   Download

In 1850, Puiseux solved the problem of finding roots of complex polynomials in two variables and proved that the field of these series is algebraically closed. His proof provided an algorithm constructing the roots.

13p viberkshire 09-08-2023 7 4   Download

Continued part 1, part 2 of ebook "A pythagorean introduction to number theory: Right triangles, sums of squares, and arithmetic" has presents the following content: advanced topics; counting pythagorean triples modulo an integer; how many lattice points are there on a circle or a sphere; what about geometry; another proof of the four squares theorem; quadratic forms and sums of squares; how many pythagorean triples are there; how are rational points distributed, really;...

143p dieptieuung 20-07-2023 4 3   Download

This book "Computational complexity: A modern approach" aims to describe such recent achievements of complexity theory in the context of more classical results. It is intended to both serve as a textbook and as a reference for self-study. Part 1 of book provide students with knowledge about: lower bounds for concrete computational models; advanced topics; communication complexity; algebraic computation models; hardness amplification and error correcting codes; proofs of PCP theorems and the Fourier transform technique;...

269p britaikridanik 05-07-2022 14 4   Download

In the paper "Liouville-type theorems for a quasilinear elliptic equation of the H´enon-type", We consider the H´enon-type quasilinear elliptic equation −Δmu = |x| aup where Δmu = div(|∇u| m−2∇u), m > 1, p>m − 1 and a ≥ 0. We are concerned with the Liouville property, i.e. the nonexistence of positive solutions in the whole space RN . We prove the optimal Liouville-type theorem for dimension N

13p runordie3 27-06-2022 6 3   Download

Advanced Algorithms Analysis and Design - Lecture 29: Proof (Breadth first search algorithm) & Depth first search. In this lecture we will cover the following: depth first search techniques is discussed; algorithms is designed; correctness of depth first search is given; topological sort and its benefits; computing strongly connected components; applications and conclusion;...

38p andromedashun 26-05-2022 6 1   Download

Advanced Algorithms Analysis and Design - Lecture 30: Proof (white path theorem) & Applications of depth first search. In this lecture we will cover the following: algorithm depth first search; classification of edges; white-path theorem; topological sort; strongly connected components;...

22p andromedashun 26-05-2022 10 1   Download

Advanced Algorithms Analysis and Design - Lecture 39: Number theoretic algorithms (Theorems and algorithms). In this lecture we will cover the following: some more proofs; GCD as a linear combination; finding GCD, a recursive theorem; Euclid’s algorithm; extended Euclid’s algorithm; time complexity of Euclid’s algorithm;...

36p andromedashun 26-05-2022 16 1   Download

Lecture Theory of Automata: Lesson 11. The main topics covered in this chapter include: proof of Kleene’s theorem part II (method with different steps), particular examples of TGs to determine corresponding Res, the following particular examples of TGs,...

21p wangziyi_1307 26-04-2022 12 2   Download

Lecture Theory of Automata: Lesson 19. The main topics covered in this chapter include: NFA corresponding to Closure of FA and examples, memory required to recognize a language and example, distinguishing one string from another and example, theorem and proof,...

20p wangziyi_1307 26-04-2022 11 2   Download

Lecture Theory of Automata: Lesson 24. The main topics covered in this chapter include: regular languages, complement of a language, theorem proof and example, intersection of two regular languages, converting final states to non-final states and old non-final states to final states,...

22p wangziyi_1307 26-04-2022 13 2   Download

Lecture Theory of Automata: Lesson 26. The main topics covered in this chapter include: example of non regular language, pumping lemma version I, proof and examples, the corresponding transition diagram may be as follows, the observations made from this example, generalize the theorem regarding the infinite regular language as follows,...

29p wangziyi_1307 26-04-2022 13 2   Download

Lecture Theory of Automata: Lesson 27. The main topics covered in this chapter include: pumping lemma version II, proof and examples, Myhill Nerode theorem and examples, strings belonging to same class, consider the language L of strings,...

14p wangziyi_1307 26-04-2022 15 2   Download

Lecture Theory of Automata: Lesson 29. The main topics covered in this chapter include: example of prefixes of a language, theorem: pref(Q in R) is regular proof and example, decidability, deciding whether two languages are regular or not, method 1 and example, method 2 and example,...

25p wangziyi_1307 26-04-2022 8 2   Download