Technical Books

The contents include, Mathematical Notation and Symbols, Indices, Simplification and Factorisation, Arithmetic of Algebraic Fractions, Formulae and Transposition.

The contents include, Preliminaries About the Integers, Polynomials, and Matrices, Vector Spaces Over Q, R, and C, Innerproduct Spaces, Groups and Group Actions, Theory of a Single Linear Transformation, Multilinear Algebra, Advanced Group Theory,. Commutative Rings and Their Modules, Fields and Galois Theory, Modules Over Noncommutative Rings.

This PDF Lectures covers the following topics related to Elementary Algebra, Foundations, Solving Linear Equations and Inequalities, Math Models, Graphs, Systems of Linear Equations, Polynomials, Factoring, Rational Expressions and Equations, Roots and Radicals, Quadratic Equations.

This note covers some algebra, Algebraic sets, More algebra, Halberts nullstellensatz, Topology of affine algebraic sets, A brief detour into plane curves, Quasiprojective varieties, Plane projective curves and bezouts theorems.

This book contains below topics, Prerequisites, Equations and Inequalities, Functions, Linear Functions, Polynomial and Rational Functions, Exponential and Logarithmic Functions, Systems of Equations and Inequalities, Analytic Geometry, Sequences Probability and Counting Theory.

This book contains below topics, The Verbal Method, Use a sentence to dene a set, The Integers, The Real Numbers, R xx possesses a decimal representation.

Major topics topics coverd are, Absolute values on fields, Ostrowskis classification of absolute values on U, Cauchy sequences and completion, Inverse limits,Properties of Zp, The field of P Adic numbers, Padic expansions, Hensels lemma, Finite fields, Profinite groups, Affine varieties, Morphisms and rational maps, Quadratic forms, Rational points on conics and Valuations on the function field of a curve.

The aim of these notes is to describe some examples of modular forms whose Fourier coefficients involve quantities from arithmetical algebraic geometry.

This PDF Lectures covers the following topics related to Arithmetic Geometry, Operations with modules, Schemes and projective schemes, Rings of dimension one, The compactified Picard group of an order of a number field, Different, discriminant and conductor, The classic theorems of the algebraic number theory, Heights of rational points on a scheme over a number field.

This PDF Lectures covers the following topics related to Arithmetic and Algebraic Geometry, Rings, Spectra, Affine Varieties, Projective Varieties, Regularity, Curves.

This note explains the following topics, Notations and conventions, Absolute cohomology and purity, Functoriality instable homotopy, Absolute cohomology, Absolute purity, Analytical invariance, Orientation and characteristic classes, Orientation theory and Chern classes, Thom classes and MGL modules, Fundamental classes, Intersection theory, Gysin morphisms and localization long exact sequence, Residues and the case of closed immersions, Projective lci morphisms, Uniqueness, Riemann Roch formulas, Todd classes, The case of closed immersions, The general case, Principle of computation, Change of orientation, Universal formulas and the Chern character, Residues and symbols, Residual Riemann Roch formula The axiomatic of Panin revisited Axioms for arithmetic cohomologies and and nbsp,Etale cohomology.

This note covers introduction, p adic numbers, Newton polygons, Multiplicative seminorms and berkovich space, The berkovich affine and projective line, Analytic spaces and function, Berkovich spaces of curves and integration.

This book contains below topics, Two disciplines of identification, Ring coherence and suspended evaluation, Foundational motivations for quantitative identity, Quantitative categories and Lawvere enrichment, The labeled quantitative 2 1 category, The Jstructure and controlled elimination, Comparison problems and the descent obstruction, Anabelian packages a quantitative category from practice, Elliptic packages and the discriminant height, The Kummerian cost protocol, An intensional Szpiro inequality, An explicit example, Descent to a presettheoretic universe, Formalization sketches in Coq, An intensional statement of the Birch and SwinnertonDyer conjecture, The Tate Shafarevich group.

This note contains below topics, General Introduction, Kronecker s Rationality Criteria and Grothendieck s pCurvature Conjecture, Density of Special Loci, Rigid Local Systems and FIsocrystals, Rigid Local Systems FontaineLaffaille modules and Crystalline Local Systems.

The aim of these notes is to describe modular forms whose Fourier coefficients involve quantities from arithmetic algebraic geometry. The examples suggest an arithmetic analogue of theta series, and a formula that relates averages of them to special values of derivatives of Eisenstein series.