Proof theory

Ebook "Complexity & cryptography: An introduction" provides that knowledge, combining an informal style with rigorous proofs of the key results to give an accessible introduction. It comes with plenty of examples and exercises (many with hints and solutions), and is based on a highly successful course developed and taught over many years to undergraduate and graduate students in mathematics and computer science.

305p zizaybay1103 29-05-2024 5 2   Download

Cryptography is concerned with the conceptualization, definition, and construction of computing systems that address security concerns. The design of cryptographic systems must be based on firm foundations. This book presents a rigorous and systematic treatment of the foundational issues: defining cryptographic tasks and solving new cryptographic problems using existing tools. It focuses on the basic mathematical tools: computational difficulty (one-way functions), pseudorandomness, and zero-knowledge proofs.

393p zizaybay1103 29-05-2024 4 2   Download

Part 1 book "Discrete mathematics and its applications" includes content: The foundations - logic and proofs; basic structures - sets, functions, sequences, sums, and matrices; algorithms; number theory and cryptography, induction and recursion; counting; discrete probability.

521p muasambanhan06 01-02-2024 4 1   Download

Part 1 book "Discrete mathematics" includes content: Sets and logic; proofs; functions, sequences, and relations; algorithms; introduction to number theory; counting method sand the pigeonhole principle.

347p muasambanhan05 16-01-2024 2 0   Download

Part 1 book "Discrete mathematics and its applications" includes content: The foundations - logic and proofs; basic structures - sets, functions, sequences, sums, and matrices; algorithms; number theory and cryptography; induction and recursion; counting; discrete probability; advanced counting techniques; relations.

593p muasambanhan05 16-01-2024 4 0   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

The book consists of five chapters. Chapter 1, Mathematical Background; Chapter 2, Formal Languages; Chapter 3, Regular Languages; Chapter 4, Context-free Languages; Chapter 5, Recursive and Recursively Enumerable Languages.

288p haojiubujain08 01-11-2023 5 2   Download

Complexity Theory is a central field of the theoretical foundations of computer science. It is concerned with the general study of the intrinsic complexity of computational tasks; that is, it addresses the question of what can be achieved within limited time (and/or with other limited natural computational resources). This book offers a conceptual perspective on Complexity Theory. It is intended to serve as an introduction for advanced undergraduate and graduate students, either as a textbook or for self-study.

632p haojiubujain07 20-09-2023 10 4   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 "Combinatorics: Topics techniques algorithms" aimed at second-year undergraduates to beginning graduates. It stresses common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter and also stresses the fact that a constructive or algorithmic proof is more valuable than an existence proof.

367p tichhythan 17-08-2023 6 4   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

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

Continued part 1, part 2 of book "A Practical Introduction to: Data Structures and Algorithm Analysis (Third Edition - Java Version)" provide with knowledge about: searching; indexing; advanced data structures; terminology and representations; graph implementations; lists and arrays revisited; advanced tree structures; theory of algorithms; analysis techniques; lower bounds; patterns of algorithms; limits to computation;...

285p britaikridanik 05-07-2022 23 5   Download

Advanced Algorithms Analysis and Design - Lecture 38: Number theoretic algorithms (Definitions and some important results). In this lecture we will cover the following: applications of number theory; divisibility; numbers; prime numbers; relatively prime numbers; GCD; partitioning of Integers; congruency classes; proofs of some results;...

38p andromedashun 26-05-2022 8 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 22. The main topics covered in this chapter include: applications of complementing and incrementing machines, equivalent machines, moore equivalent to mealy, proof and example, mealy equivalent to moore, proof and example,...

25p wangziyi_1307 26-04-2022 16 2   Download