1、伯克利主页门户--学术(Academics)--班级安排和课程(Courses)：

----Schools & Colleges，大学的院系，是学生视角最能感受到的划分。

----Academic departments，大学的学术部门，是学校管理老师的划分维度，也是给老师门分配工作空间/教学楼的维度，比如数学老师就到数学楼上课，计算机老师到计算机楼去教课。当然这个不会绝对，老师大概也有可能去不同的楼去教课。

----学生选课，就通过绑定的{课程-上课地点}选择了上课地点，走到不同的地点上课。

2、班级和选课门户--课程全表(Course Catalog)：

----选课的搜索查找有多种，包括按主题搜索(Subjects Search)，按关键字搜索(Keyword Search)，按主修专业的要求来查找(Major Requirements Search)，按照导师来查找(Instructor Search)。

----顶部菜单有Class Schedule、Course Catalog、Undergraduate、Graduate几个维度。这里要查看全部课程，点选Course Catalog进入，如下。

3、课程全表概览：

----本科生(Undergraduate)课程一共有6772门。

----研究生(Graduate)课程一共有4398门。

----总共的课程有11170门，超过一万门！

5、看一下数学课程：

----在Department里面可以选各个专业课的类别，比如图中以此是：语言学(Linguistics)、材料科学与工程(Materias Science & Eng)、Mathematics(数学)、Mechanical Engineering(机械工程)。

----在Department之上是Undergraduate(本科生)和Graduate(研究生)的课程层次区分。这个层次的标题叫Academic Career(学术生涯)。国内有些大学有研究生院，和通常的以本科教育为主的各院系并列，但在学术层次上是高一阶的。

6、数学本科课程一共有80下图为前40门。

----32行：傅里叶分析以及小波和信号处理，小波的英文是Wavelets，原来小波不是某个中文名的小波命名的。和Wavelets相近，在数据通信里有一个Flowlet的技术，把TCP流(stream)切分成时间片上的子流称为Flowlet。可以拿这两个词相互对照一下增加对概念的理解。

6、数学本科课程一共有80下图为后40门。

----这个课程里面有两个很有意思的课程，是中学数学课程1和中学数学课程2。这是在大学里为中学-大学的学习衔接而准备的课程。

----中学数学课程1的Course Description：Theory of rational numbers based on the number line, the Euclidean algorithm and fractions in lowest terms. The concepts of congruence and similarity, equation of a line, functions, and quadratic functions.  //这个内容来看似乎是初中数学的内容。

----中学数学课程2的Course Description：Complex numbers and Fundamental Theorem of Algebra, roots and factorizations of polynomials, Euclidean geometry and axiomatic systems, basic trigonometry. //这个内容接近高中数学的内容。

----低阶数学课程的描述：This course aims to bring students with varying Math backgrounds up-to-speed with the expectations of UC Berkeley’s lower division mathematics courses. This course will support comprehension of the fundamental concepts necessary to excel in Math 16A/16B, 1A/1B, 10A/10B, and beyond. You can take this prep course concurrently with or prior to your Calculus classes. The course curriculum covers algebraic operations, laws of exponents and logarithms, inequalities and absolute values, single-variable function properties, polynomials, power and exponential functions, logarithmic functions, trigonometric functions, coordinate geometry in two and three dimensions, complex numbers, and functions of several variables.

----数学史课程的Course Description：History of algebra, geometry, analytic geometry, and calculus from ancient times through the seventeenth century and selected topics from more recent mathematical history.

----数学方法课程的Course Description：The sequence Math 10A, Math 10B is intended for majors in the life sciences. Introduction to differential and integral calculus of functions of one variable, ordinary differential equations, and matrix algebra and systems of linear equations.

----预科微积分课程描述：Polynomial and rational functions, exponential and logarithmic functions, trigonometry and trigonometric functions. Complex numbers, fundamental theorem of algebra, mathematical induction, binomial theorem, series, and sequences. 

7、数学研究生课程--一共有70门下图为前50门

----这里有相当多的课程，大概是数学专业研究生才会学的，比如到了群论环论数论模型论集合论，都含有一个Theory，有纯数学理论的味道，大概率都是数学专业才需要的课程。

----有一门冯诺依曼代数(Von Neumann Algebras)，虽然也知道冯诺依曼不仅是计算机架构的开创者，也是数学大师，但冯诺依曼代数作为一门学科课程却少听到(比如说冯诺依曼代数的书)。查一下如下。////冯诺依曼代数（von Neumann algebra）是由约翰·冯·诺伊曼及其合作者在1930年代创立的算子环理论成果。冯诺依曼代数是希尔伯特空间上有界算子构成的自伴代数，在弱算子拓扑下封闭，并包含单位算子，是算子代数理论的重要分支。

7、数学研究生课程--一共有70门下图为后20门

----从48到56，都是一些专题课，是由导师选定的主题(Advanced topics chosen by the instructor)，来看一下这些出题：数值分析专题，代数，应用数学，拓扑学，微分几何，数学分析，偏微分方程。

----常微分方程ODE：Rigorous theory of ordinary differential equations. Fundamental existence theorems for initial and boundary value problems, variational equilibria, periodic coefficients and Floquet Theory, Green's functions, eigenvalue problems, Sturm-Liouville theory, phase plane analysis, Poincare-Bendixon Theorem, bifurcation, chaos.

----偏微分方程：The theory of boundary value and initial value problems for partial differential equations, with emphasis on nonlinear equations. Laplace's equation, heat equation, wave equation, nonlinear first-order equations, conservation laws, Hamilton-Jacobi equations, Fourier transform, Sobolev spaces.

----复变函数：Normal families. Riemann Mapping Theorem. Picard's theorem and related theorems. Multiple-valued analytic functions and Riemann surfaces. Further topics selected by the instructor may include: harmonic functions, elliptic and algebraic functions, boundary behavior of analytic functions and HP spaces, the Riemann zeta functions, prime number theorem.

----模型论：Syntactical characterization of classes closed under algebraic operations. Ultraproducts and ultralimits, saturated models. Methods for establishing decidability and completeness. Model theory of various languages richer than first-order.

----集合论：Axiomatic foundations. Operations on sets and relations. Images and set functions. Ordering, well-ordering, and well-founded relations; general principles of induction and recursion. Ranks of sets, ordinals and their arithmetic. Set-theoretical equivalence, similarity of relations; definitions by abstraction. Arithmetic of cardinals. Axiom of choice, equivalent forms, and consequences. Sequence begins fall.

----群论：Topics such as: generators and relations, infinite discrete groups, groups of Lie type, permutation groups, character theory, solvable groups, simple groups, transfer and cohomological methods.

----概率论：The course is designed as a sequence with Statistics C205B/Mathematics C218B with the following combined syllabus. Measure theory concepts needed for probability. Expection, distributions. Laws of large numbers and central limit theorems for independent random variables. Characteristic function methods. Conditional expectations, martingales and martingale convergence theorems. Markov chains. Stationary processes. Brownian motion.

----谐波分析：Basic properties of Fourier series, convergence and summability, conjugate functions, Hardy spaces, boundary behavior of analytic and harmonic functions. Additional topics at the discretion of the instructor.

8、Berkeley的数学和统计学在一个大楼里

9、伯克利大学的校园大概这样：

小结：本文概览了加州大学伯克利分校的大学课程列表，全校提供的课程超过1万门，其中本科生课程6700，研究生课程4400，供不同院系的学生选择。以数学为例，其中本科生课程超过80门，研究生课程超过70门。比较有意思的是，大学本科数学课程中，有2门中学数学课程(Mathematics of the Secondary School Curriculum)，包含了初中和高中数学，还有低阶数学课程、微积分预科的课程，这对于高中大学衔接是有帮助的，国内学校或可以参考，开一些基础衔接的预科课程，把高中-大学的衔接起来，供有需要的学生参加。

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摘要：加州大学伯克利分校课程体系概览：全校开设11170门课程，包括6772门本科生课程和4398门研究生课程。数学系开设80门本科课程和70门研究生课程，涵盖从中学衔接课程到高阶理论课程。特别值得注意的是设有2门中学数学衔接课程（涵盖初高中内容）以及预科微积分等过渡性课程，为不同基础的学生提供学习支持。研究生课程则包含群论、模型论等专业理论课程。这种课程设置既保证了学术深度，又注重教育衔接，值得国内高校借鉴。