伯克利课程观察：1万门课程总览+200门数学课程概览

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 DescriptionTheory 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 DescriptionComplex 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 varyingMath 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 courseconcurrently 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 DescriptionHistory 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 DescriptionThe sequence Math 10A, Math 10B isintended 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ODERigorous theoryofordinary differential equations.Fundamental existence theoremsfor initial and boundary value problems, variational equilibria, periodic coefficients andFloquet Theory, Greens 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 problemsforpartial differential equations, with emphasis on nonlinear equations.Laplaces 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. Picards 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 theoryconcepts needed for probability. Expection, distributions.Laws of large numbers and central limit theoremsfor 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。完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。