· [ ] · Thư Viện Thuật Ngữ Chuyên Ngành, có lý giải sơ lược về các khái niệm

Gần như mọi thuật ngữ trong khoa học đều có thể tìm thấy lời giải thích cụ thể ở đây:

http://en2.wikipedia.org/

Ví dụ- một bài giới thiệu sơ qua cho các ngành tóan học :

http://en2.wikipedia.org/wiki/Mathematics

Overview and history of mathematics
See the article on the history of mathematics for details.
The word "mathematics" comes from the Greek μάθημα (máthema) which means "science, knowledge, or learning"; μαθηματικός (mathematikós) means "fond of learning".

The major disciplines within mathematics arose out of the need to do calculations in commerce, to measure land and to predict astronomical events. These three needs can be roughly related to the broad subdivision of mathematics into the study of structure, space and change.

The study of structure starts with numbers, firstly the familiar natural numbers and integers and their arithmetical operations, which are recorded in elementary algebra. The deeper properties of whole numbers are studied in number theory. The investigation of methods to solve equations leads to the field of abstract algebra, which, among other things, studies rings and fields, structures that generalize the properties possessed by the familiar numbers. The physically important concept of vector, generalized to vector spaces and studied in linear algebra, belongs to the two branches of structure and space.

The study of space originates with geometry, first the Euclidean geometry and trigonometry of familiar three-dimensional space, but later also generalized to non-Euclidean geometries which play a central role in general relativity. Several long standing questions about ruler and compass constructions were finally settled by Galois theory. The modern fields of differential geometry and algebraic geometry generalize geometry in different directions: differential geometry emphasizes the concepts of functions, fiber bundles, derivatives, smoothness and direction, while in algebraic geometry geometrical objects are described as solution sets of polynomial equations. Group theory investigates the concept of symmetry abstractly and provides a link between the studies of space and structure. Topology connects the study of space and the study of change by focusing on the concept of continuity.

Understanding and describing change in measurable quantities is the common theme of the natural sciences, and calculus was developed as a most useful tool for doing just that. The central concept used to describe a changing variable is that of a function. Many problems lead quite naturally to relations between a quantity and its rate of change, and the methods to solve these are studied in the field of differential equations. The numbers used to represent continuous quantities are the real numbers, and the detailed study of their properties and the properties of real-valued functions is known as real analysis. For several reasons, it is convenient to generalise to the complex numbers which are studied in complex analysis. Functional analysis focuses attention on (typically infinite-dimensional) spaces of functions, laying the groundwork for quantum mechanics among many other things. Many phenomena in nature can be described by dynamical systems and chaos theory deals with the fact that many of these systems exhibit unpredictable yet deterministic behavior.

In order to clarify and investigate the foundations of mathematics, the fields of set theory, mathematical logic and model theory were developed.

When computers were first conceived, several essential theoretical concepts were shaped by mathematicians, leading to the fields of computability theory, computational complexity theory, information theory and algorithmic information theory. Many of these questions are now investigated in theoretical computer science. Discrete mathematics is the common name for those fields of mathematics useful in computer science.

An important field in applied mathematics is statistics, which uses probability theory as a tool and allows the description, analysis and prediction of phenomena and is used in all sciences. Numerical analysis investigates the methods of efficiently solving various mathematical problems numerically on computers and takes rounding errors into account.


Topics in mathematics
An alphabetical list of mathematical topics is available; together with the "Watch links" feature, this list is useful to track changes in mathematics articles. The following list of subfields and topics reflects one organizational view of mathematics.


Quantity
Numbers -- Natural numbers -- Integers -- Rational numbers -- Real numbers -- Complex numbers -- Hypercomplex numbers -- Quaternions -- Octonions -- Sedenions -- Hyperreal numbers -- Surreal numbers -- Ordinal numbers -- Cardinal numbers -- p-adic numbers -- Integer sequences -- Mathematical constants -- Number names -- Infinity

Change
Arithmetic -- Calculus -- Vector calculus -- Analysis -- Differential equations -- Dynamical systems and chaos theory -- Fractional calculus -- List of functions

Structure
Abstract algebra -- Number theory -- Algebraic geometry -- Group theory -- Monoids -- Analysis -- Topology -- Linear algebra -- Graph theory -- Universal algebra -- Category theory

Space
Topology -- Geometry -- Trigonometry -- Algebraic geometry -- Differential geometry -- Differential topology -- Algebraic topology -- Linear algebra -- Fractal geometry

Discrete mathematics
Combinatorics -- Naive set theory -- Probability -- Theory of computation -- Finite mathematics -- Cryptography -- Graph theory -- Game theory

Applied Mathematics
Mechanics -- Numerical analysis -- Optimization -- Probability -- Statistics

Famous Theorems and Conjectures
Fermat's last theorem -- Riemann hypothesis -- Continuum hypothesis -- P=NP -- Goldbach's conjecture -- Twin Prime Conjecture -- Gödel's incompleteness theorems -- Poincaré conjecture -- Cantor's diagonal argument -- Pythagorean theorem -- Central limit theorem -- Fundamental theorem of calculus -- Fundamental theorem of algebra -- Fundamental theorem of arithmetic -- Four color theorem -- Zorn's lemma -- "The most remarkable formula in the world" -- Axiom of countability

Foundations and Methods
Philosophy of mathematics -- Mathematical intuitionism -- Mathematical constructivism -- Foundations of mathematics -- Set theory -- Symbolic logic -- Model theory -- Category theory -- Theorem-proving -- Logic -- Reverse Mathematics -- Table of mathematical symbols

History and the World of Mathematicians
History of mathematics -- Timeline of mathematics -- Mathematicians -- Fields medal -- Abel Prize -- Millennium Prize Problems (Clay Math Prize) -- International Mathematical Union -- Mathematics competitions -- Lateral thinking

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Applied Mathematics
Mechanics -- Numerical analysis -- Optimization -- Probability -- Statistics

Đồng chí Bu định theo ngành nào .Lý thuyết hay ứng dụng ?
Vừa rồi em có gặp một bác tiến sĩ hiện làm ở viện toán Hung ,bảo bác ơi sao bác giỏi thế .Bác ấy cười : hồi đi học mình cũng thuộc dạng học dốt nên mới chọn cái algebra là cái dễ nhất trong toán chứ có giỏi giang gì .Cái ấy đúng là có vẻ khoai khoai và dễ nhất thật ,phải không đồng chí Bu ?

Vấn đề cơ bản của Algebra hiện đại lại chính là vấn đề nền tảng chung của các hệ thống tóan học- đó là các vấn đề về cấu trúc đại số (Structure) như trường số, vành số, lý thuyết category, lý thuyết topoi, các phân lớp nghiệm, đại diện lớp, bất biến trong hệ thống của các lọai phương trình từ Diophanne cho tới các dạng phức tạp hơn v.v. Algebra là thứ cơ bản nhất chứ không hề dễ nhất vì nói chung không có ngành Tóan nào là phức tạp nhất- chỉ có giới hạn khả năng phát triển của con người đối với các ngành Tóan khác nhau hiện nay ở mức độ nào so với nhau mà thôi (bác tiến sĩ Tóan ấy nói đùa đấy). Hầu như trong mọi ngành tóan, Algebra luôn có mặt và là cột sống cho chúng bởi vì nó nghiên cứu phần khung xương (Structure) cho các lọai tóan khác.

Trường tớ (hay Berlin nói chung) cũng là một trung tâm mạnh về tóan ứng dụng, cũng tương tự như Budapest chỗ cậu. Các hướng chính mà Berlin và Budapest mạnh là tóan rời rạc (bao gồm cả tóan tổ hợp, hình học tổ hợp, lý thuyết Graph, mạng lưới, các lý thuyết tối ưu hóa .v.v.). Tớ giờ cũng học tóan rời rạc, nhưng chưa biết rõ nên theo hướng nào trong mấy hướng nhỏ là tối ưu tổ hợp, hay hình học tổ hợp. Nói chung học để biết nói chuyện cho vui ấy mà, chứ làm sao mà đấu được với người khác.