Advanced Number Theory
ພ.ພ. 2012 · Courier Corporation
3,0star
1 ຄຳຕິຊົມreport
ປຶ້ມອີບຸກ
288
ໜ້າ
reportບໍ່ໄດ້ຢັ້ງຢືນການຈັດອັນດັບ ແລະ ຄຳຕິຊົມ ສຶກສາເພີ່ມເຕີມ
ກ່ຽວກັບປຶ້ມ e-book ນີ້
"A very stimulating book ... in a class by itself." — American MathematicalMonthly
Advanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject.
The book is divided into three parts. Part I is concerned with background material — a synopsis of elementary number theory (including quadratic congruences and the Jacobi symbol), characters of residue class groups via the structure theorem for finite abelian groups, first notions of integral domains, modules and lattices, and such basis theorems as Kronecker's Basis Theorem for Abelian Groups.
Part II discusses ideal theory in quadratic fields, with chapters on unique factorization and units, unique factorization into ideals, norms and ideal classes (in particular, Minkowski's theorem), and class structure in quadratic fields. Applications of this material are made in Part III to class number formulas and primes in arithmetic progression, quadratic reciprocity in the rational domain and the relationship between quadratic forms and ideals, including the theory of composition, orders and genera. In a final concluding survey of more recent developments, Dr. Cohn takes up Cyclotomic Fields and Gaussian Sums, Class Fields and Global and Local Viewpoints.
In addition to numerous helpful diagrams and tables throughout the text, appendices, and an annotated bibliography, Advanced Number Theory also includes over 200 problems specially designed to stimulate the spirit of experimentation which has traditionally ruled number theory.
Advanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject.
The book is divided into three parts. Part I is concerned with background material — a synopsis of elementary number theory (including quadratic congruences and the Jacobi symbol), characters of residue class groups via the structure theorem for finite abelian groups, first notions of integral domains, modules and lattices, and such basis theorems as Kronecker's Basis Theorem for Abelian Groups.
Part II discusses ideal theory in quadratic fields, with chapters on unique factorization and units, unique factorization into ideals, norms and ideal classes (in particular, Minkowski's theorem), and class structure in quadratic fields. Applications of this material are made in Part III to class number formulas and primes in arithmetic progression, quadratic reciprocity in the rational domain and the relationship between quadratic forms and ideals, including the theory of composition, orders and genera. In a final concluding survey of more recent developments, Dr. Cohn takes up Cyclotomic Fields and Gaussian Sums, Class Fields and Global and Local Viewpoints.
In addition to numerous helpful diagrams and tables throughout the text, appendices, and an annotated bibliography, Advanced Number Theory also includes over 200 problems specially designed to stimulate the spirit of experimentation which has traditionally ruled number theory.
ການຈັດອັນດັບ ແລະ ຄຳຕິຊົມ
3,0
1 ຄຳຕິຊົມ
ໃຫ້ຄະແນນ e-book ນີ້
ບອກພວກເຮົາວ່າທ່ານຄິດແນວໃດ.
ອ່ານຂໍ້ມູນຂ່າວສານ
ສະມາດໂຟນ ແລະ ແທັບເລັດ
ຕິດຕັ້ງ ແອັບ Google Play Books ສຳລັບ Android ແລະ iPad/iPhone. ມັນຊິ້ງຂໍ້ມູນໂດຍອັດຕະໂນມັດກັບບັນຊີຂອງທ່ານ ແລະ ອະນຸຍາດໃຫ້ທ່ານອ່ານທາງອອນລາຍ ຫຼື ແບບອອບລາຍໄດ້ ບໍ່ວ່າທ່ານຈະຢູ່ໃສ.
ແລັບທັອບ ແລະ ຄອມພິວເຕີ
ທ່ານສາມາດຟັງປຶ້ມສຽງທີ່ຊື້ໃນ Google Play ໂດຍໃຊ້ໂປຣແກຣມທ່ອງເວັບຂອງຄອມພິວເຕີຂອງທ່ານໄດ້.
eReaders ແລະອຸປະກອນອື່ນໆ
ເພື່ອອ່ານໃນອຸປະກອນ e-ink ເຊັ່ນ: Kobo eReader, ທ່ານຈຳເປັນຕ້ອງດາວໂຫຼດໄຟລ໌ ແລະ ໂອນຍ້າຍມັນໄປໃສ່ອຸປະກອນຂອງທ່ານກ່ອນ. ປະຕິບັດຕາມຄຳແນະນຳລະອຽດຂອງ ສູນຊ່ວຍເຫຼືອ ເພື່ອໂອນຍ້າຍໄຟລ໌ໄໃສ່ eReader ທີ່ຮອງຮັບ.