Technical Books

This PDF covers the following topics related to Numerical Analysis, Series and Sequences, Integrals as Sums and Derivatives as Differences, Interpolation, Nonlinear Equations, Methods for Ordinary Differential Equations, Fourier Analysis, Spectral Interpolation, Differentiation, Quadrature.

This note contains below topics, Motivation and Overview, Iterative KrylovSubspace Solvers, Computing the Cholesky Factorization of Sparse Matrices, Symmetric DiagonallyDominant Matrices and Graphs, Augmented SpanningTree Preconditioners, Linear Algebra Notation and Definitions.

Numerical computation underpins almost all of modern scientific and industrial research and development. This book contains below topics, Probabilistic Numerical Methods, DecisionTheoretic Treatment, Numerical Disintegration, Computational Pipelines and PNM, Numerical Experiments, A Proofs, S1 Philosophical Status of the Belief Distribution, S2 Existence of NonRandomised Bayes Rule, S3 Optimal Information A Counterexample, S4 Monte Carlo Methods for Numerical Disintegration, S5 Truncation of the Prior Distribution Proof of Theorem 4.8.

Robert Daniel Carmichael March 1, 1879 May 2, 1967 was a leading American mathematician.The purpose of this little book is to give the reader a convenient introduction to the theory of numbers, one of the most extensive and most elegant disciplines in the whole body of mathematics. The arrangement of the material is as follows, The five chapters are devoted to the development of those elements which are essential to any study of the subject. The sixth and last chapter is intended to give the reader some indication of the direction of further study with a brief account of the nature of the material in each of the topics suggested.

This note explains the following topics, Divisibility, Multiplicative functions, Modular arithmetic, Primitive roots, Quadratic residues, Diophantine equations, Quadratic number fields, Chebyshevs theorem.

This book contains below topics, Prime Numbers, The Ring of Integers Modulo n, Public key Cryptography, Quadratic Reciprocity, Continued Fractions, Elliptic Curves.

This brief collects notes on elementary and medium level number theory, mainly for computer science students. It can support a discrete mathematics course, a foundations course, or a cryptography course. The opening chapters cover divisibility, primes, modular arithmetic, and Eulers totient function.

This note contains below topics, Analytic Theory, The Arithmetic Theory, III CMMotives, Applications, A Additional Notes Solutions to the Exercises, B Summary, Index of definitions.

This book contains below topics, Local Class Field Theory LubinTate Theory, The Cohomology of Groups, III Local Class Field Theory Cohomology, Brauer Groups, V Global Class Field Theory Statements, VI LSeries and the Density of Primes, VII Global Class Field Theory Proofs, VIII Complements, A Exercises, B Solutions to Exercises, C Sources for the history of class field theory.

This book contains below topics, A First Course in Modular Forms, Springer GUNNING, Introduction to Elliptic Curves and Modular Forms, Elliptic Curves, Booksurge Available on my website MIYAKE, Cours dArithmetique, Presses Univ de France The last.

This is an online resource on multivariable calculus. This deals with following topics, Fundamental Theorems, Capstone and The Inverse Square Law.

This note covers the following topics, Vectors and the geometry of space, Directional derivatives, gradients, tangent planes, introduction to integration, Integration over nonrectangular regions, Integration in polar coordinates, applications of multiple integrals, surface area, Triple integration, Spherical coordinates, The Fundamental Theorem of Calculus for line integrals, Greens Theorem, Divergence and curl, Surface integrals of scalar functions, Tangent planes, introduction to flux, Surface integrals of vector fields, The Divergence Theorem.

This note explains the following topics, Analytic Geometry, Instantaneous Rate of Change, The Derivative, Rules for Finding Derivatives, Transcendental Functions, Curve Sketching, Applications of the Derivative, Integration, Techniques of Integration, Applications of Integration, Polar Coordinates, Parametric Equations, Sequences and Series, Vector Functions, Partial Differentiation, Multiple Integration, Vector Calculus, Differential Equations.

This book contains below topics, Parametric Equations and Polar Coordinates, Vectors in Space, Vector Valued Functions, Differentiation of Functions of Several Variables, Multiple Integration, Vector Calculus, Second Order Differential Equations.

This book contains below topics, Huber rings, Twisted principal parts in several variables and coordinates, Twisted Connections, Twisted differential operators of infinite level, Twisted calculus of finite radius.