Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.

Curves, Algebraic. --- Finite fields (Algebra) --- Modular fields (Algebra) --- Algebra, Abstract --- Algebraic fields --- Galois theory --- Modules (Algebra) --- Algebraic curves --- Algebraic varieties --- Abelian group. --- Abelian variety. --- Affine plane. --- Affine space. --- Affine variety. --- Algebraic closure. --- Algebraic curve. --- Algebraic equation. --- Algebraic extension. --- Algebraic function. --- Algebraic geometry. --- Algebraic integer. --- Algebraic number field. --- Algebraic number theory. --- Algebraic number. --- Algebraic variety. --- Algebraically closed field. --- Applied mathematics. --- Automorphism. --- Birational invariant. --- Characteristic exponent. --- Classification theorem. --- Clifford's theorem. --- Combinatorics. --- Complex number. --- Computation. --- Cyclic group. --- Cyclotomic polynomial. --- Degeneracy (mathematics). --- Degenerate conic. --- Divisor (algebraic geometry). --- Divisor. --- Dual curve. --- Dual space. --- Elliptic curve. --- Equation. --- Fermat curve. --- Finite field. --- Finite geometry. --- Finite group. --- Formal power series. --- Function (mathematics). --- Function field. --- Fundamental theorem. --- Galois extension. --- Galois theory. --- Gauss map. --- General position. --- Generic point. --- Geometry. --- Homogeneous polynomial. --- Hurwitz's theorem. --- Hyperelliptic curve. --- Hyperplane. --- Identity matrix. --- Inequality (mathematics). --- Intersection number (graph theory). --- Intersection number. --- J-invariant. --- Line at infinity. --- Linear algebra. --- Linear map. --- Mathematical induction. --- Mathematics. --- Menelaus' theorem. --- Modular curve. --- Natural number. --- Number theory. --- Parity (mathematics). --- Permutation group. --- Plane curve. --- Point at infinity. --- Polar curve. --- Polygon. --- Polynomial. --- Power series. --- Prime number. --- Projective plane. --- Projective space. --- Quadratic transformation. --- Quadric. --- Resolution of singularities. --- Riemann hypothesis. --- Scalar multiplication. --- Scientific notation. --- Separable extension. --- Separable polynomial. --- Sign (mathematics). --- Singular point of a curve. --- Special case. --- Subgroup. --- Sylow theorems. --- System of linear equations. --- Tangent. --- Theorem. --- Transcendence degree. --- Upper and lower bounds. --- Valuation ring. --- Variable (mathematics). --- Vector space.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-45), Volume V, will be forthcoming.

Oscillations. --- Absolute value. --- Abstract algebra. --- Affine plane. --- Affine space. --- Algebraic Method. --- Analytic function. --- Bifurcation theory. --- Big O notation. --- Canonical form. --- Cartesian coordinate system. --- Cauchy sequence. --- Characteristic exponent. --- Characteristic polynomial. --- Clockwise. --- Coefficient matrix. --- Coefficient. --- Complete theory. --- Complex conjugate. --- Complex number. --- Complex plane. --- Computation. --- Connected space. --- Continuous function. --- Control function (econometrics). --- Convex set. --- Corollary. --- Critical frequency. --- Curve. --- Degeneracy (mathematics). --- Degrees of freedom (statistics). --- Determinant. --- Differentiable function. --- Differentiable manifold. --- Differential equation. --- Dimension. --- Dimensional analysis. --- Divisor (algebraic geometry). --- Eigenvalues and eigenvectors. --- Elliptic function. --- Endomorphism. --- Equation. --- Equations of motion. --- Existence theorem. --- Existential quantification. --- Fixed point (mathematics). --- Floquet theory. --- Homeomorphism. --- Homogeneous function. --- Homotopy. --- Hyperplane. --- Hypersurface. --- Implicit function theorem. --- Interval (mathematics). --- Limit cycle. --- Limit point. --- Line element. --- Linear algebra. --- Linear differential equation. --- Linear map. --- Linear space (geometry). --- Linearity. --- Lipschitz continuity. --- Lyapunov stability. --- Manifold. --- Matrix function. --- Maxima and minima. --- Morphism. --- N-vector. --- Non-associative algebra. --- Nonlinear system. --- Optimal control. --- Orbital stability. --- Parameter. --- Parametrization. --- Periodic function. --- Piecewise. --- Probability. --- Quadratic differential. --- Quadratic function. --- Quadratic. --- Real projective plane. --- Real projective space. --- Scientific notation. --- Second derivative. --- Semicircle. --- Separatrix (mathematics). --- Sign (mathematics). --- Special case. --- Submanifold. --- Summation. --- Theorem. --- Theory. --- Topological dynamics. --- Topological space. --- Transpose. --- Two-dimensional space. --- Uniform convergence. --- Uniqueness theorem. --- Vector space. --- Zero of a function.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books exploring puzzles and brainteasers, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects brings together authors from a variety of specialties to present fascinating problems and solutions in recreational mathematics. Contributors to the book show how sophisticated mathematics can help construct mazes that look like famous people, how the analysis of crossword puzzles has much in common with understanding epidemics, and how the theory of electrical circuits is useful in understanding the classic Towers of Hanoi puzzle. The card game SET is related to the theory of error-correcting codes, and simple tic-tac-toe takes on a new life when played on an affine plane. Inspirations for the book's wealth of problems include board games, card tricks, fake coins, flexagons, pencil puzzles, poker, and so much more. Looking at a plethora of eclectic games and puzzles, The Mathematics of Various Entertaining Subjects is sure to entertain, challenge, and inspire academic mathematicians and avid math enthusiasts alike.

Mathematical recreations. --- Mathematical recreations --- Research. --- Mathematical puzzles --- Number games --- Recreational mathematics --- Recreations, Mathematical --- Puzzles --- Scientific recreations --- Games in mathematics education --- Magic squares --- Magic tricks in mathematics education --- Mathematics. --- Mathematic --- Amazing Asteroid. --- Atoll. --- Begird. --- Bernstein's Bijection. --- Chromatic Combat. --- Cookie Monster number. --- Cookie Monster. --- Devious Dice. --- Eluding Execution. --- EndGame. --- Fibonacci sequence. --- Flipping Fun. --- Flush. --- Full House. --- Get the Giraffe. --- Gilbreath numbers. --- Gilbreath permutations. --- Graeco-Latin squares. --- Hamming weight. --- Heartless Poker. --- Hex. --- Knop's puzzle. --- Leonhard Euler. --- Norman Gilbreath. --- SET. --- Sperner's Lemma. --- Straight. --- Super-n-nacci sequence. --- The Game of Y. --- The New York Times. --- Tower of Hanoi. --- Traveling Salesman Problem. --- Tribonacci sequence. --- Zeckendorf representation. --- advanced mathematics. --- affine plane. --- affine planes. --- algorithms. --- baseball. --- card effects. --- card games. --- card moves. --- card tricks. --- chess. --- coding theory. --- coin-weighing puzzles. --- connection games. --- continued fractions. --- cookies. --- coupling. --- crossword networks. --- crossword puzzle difficulty. --- crossword puzzles. --- decomposition. --- delta-to-wye transformation. --- dissection puzzles. --- divination puzzles. --- dualism. --- electrical power distribution. --- epidemics. --- error correction. --- error detection. --- error-correcting codes. --- find-and-label problem. --- flexagons. --- folding puzzles. --- game-theoretic perspective. --- generalizations. --- generator assignment. --- graphical objects. --- group structures. --- ice cream trick. --- infinite families. --- iterative stochastic process. --- just-find problem. --- linear code. --- magic tricks. --- mathematical exhibits. --- mathematical puzzles. --- maze design. --- mazes. --- minimum spanning tree. --- multiple-pans problem. --- museums. --- n-nacci sequence. --- network properties. --- network structure. --- one-move puzzles. --- packing puzzles. --- parallel scales. --- parallel weighing problem. --- period-four move. --- period-four principles. --- phyllotactic mazes. --- playing cards. --- poker. --- probability. --- random graph process. --- random moves. --- random walks. --- rearrangement puzzles. --- recreational mathematics. --- recreational problems. --- seeded stippling. --- simple objects. --- simplex. --- squash. --- surreal numbers. --- symmetries. --- tetraflexagons. --- tic-tac-toe. --- unique solutions. --- vortex tiles. --- weighing puzzles. --- winning strategies.