抽象代数 Abstract Algebra

「万门大学」抽象代数的学习笔记,欢迎指正。

Table of Contents

第1讲 集合的定义

第2讲 集合的运算

第3讲 集合间的关系

第4讲 映射

第5讲 罗素悖论(选修)

第6讲 势与基数(选修)

第7讲 定义良好

第8讲 群的定义

第9讲 子群与生成

第10讲 循环群与阶

第11讲 陪集与指数

第12讲 拉格朗日定理

第13讲 共轭与正规子群

第14讲 商群

第15讲 同态与同构

第16讲 群同构定理

第17讲 群作用

第18讲 合成列(选修)

第19讲 自由群(选修)

第20讲 稳定子,中心化, 正规化子

第21讲 类等式定理

第22讲 n次对称群

第23讲 自同构

第24讲 Z/n

第25讲 半直积

第26讲 西罗定理(选修)

第27讲 西罗定理的应用(选修)

第28讲 可解群

Course Notes

Advanced Placement

AP Macroeconomics https://macro.shawnzhong.com
AP Microeconomics https://micro.shawnzhong.com
AP Chemistry https://chem.shawnzhong.com
AP Statistics https://stats.shawnzhong.com
AP Physics C: E&M https://em.shawnzhong.com
AP Physics C: Mechanics https://mech.shawnzhong.com

Mathematics

Math 240 - Discrete Math https://shawnzhong.com/240
Math 375 - Linear Algebra https://shawnzhong.com/375
Math 431 - Intro to Probability https://shawnzhong.com/431
Math 514 - Numerical Analysis https://shawnzhong.com/514
Math 521 - Analysis I https://shawnzhong.com/521
Math 541 - Abstract Algebra https://shawnzhong.com/541
Math 632 - Stochastic Processes https://shawnzhong.com/632
Abstract Algebra @ 万门大学 https://shawnzhong.com/aa
Linear Algebra @ 万门大学 https://shawnzhong.com/la

CS/ECE 252

CS/ECE 252: Introduction to Computer Engineering Source: http://ece252.engr.wisc.edu/
Universal Computing Devices MP4 Flash
Trends and Complexity MP4 Flash
Abstraction MP4 Flash
Electrical Information MP4 Flash
Number Representation MP4 Flash
Base Conversion MP4 Flash
Counting MP4 Flash
Arithmetic MP4 Flash
Signed Numbers MP4 Flash
Sign Extension and Overflow MP4 Flash
Fixed- and Floating-Point MP4 Flash
ASCII MP4 Flash
Logic Functions MP4 Flash
Combinational Logic MP4 Flash
Combinational Building Blocks MP4 Flash
Sequential Logic and Flip-Flops MP4 Flash
Finite State Machines MP4 Flash
Registers and Memory MP4 Flash
Basic Processor Model MP4 Flash
Instructions and the Instruction Cycle MP4 Flash
LC-3 ISA and Processor Overview MP4 Flash
LC-3 Operate Instructions MP4 Flash
Simple Programs with LC-3 Operate Instructions MP4 Flash
Basic LC-3 Data Movement MP4 Flash
More LC-3 Data Movement MP4 Flash
LC-3 Control Flow MP4 Flash
Programming Techniques MP4 Flash
LC-3 Assembly Language MP4 Flash
LC-3 Memory Allocation MP4 Flash
LC-3 Assembler MP4 Flash
Subroutines MP4 Flash
Programming With Subroutines MP4 Flash
I/O Concepts MP4 Flash
LC-3 I/O MP4 Flash
Operating Systems MP4 Flash
LC-3 TRAPs MP4 Flash

CS/ECE 352

CS/ECE 352: Digital System Fundamentals Source: http://ece352.engr.wisc.edu/ 
Fundamentals Review MP4 Flash
Binary Coded Decimal, Counting MP4 Flash
Boolean Algebra MP4 Flash Slide
Standard Forms MP4 Flash Slide
Universal Gates MP4 Flash Slide
Introduction to K-Maps MP4 Flash Slide
Optimization with K-Maps MP4 Flash Slide
Don't-Cares MP4 Flash Slide
Decoders and Encoders MP4 Flash Slide
Multiplexers MP4 Flash Slide
Tristates MP4 Flash Slide
Implementation Technology MP4 Flash Slide
Arithmetic Structures MP4 Flash Slide
ALUs MP4 Flash Slide
Re-examining Carry Bits MP4 Flash Slide
Carry Look-Ahead Adders MP4 Flash Slide
D Latches and FFs MP4 Flash Slide
Intro to Sequential Circuits MP4 Flash Slide
State Diagrams MP4 Flash Slide
Sequential Circuit Design Overview MP4 Flash Slide
State Minimization MP4 Flash Slide
FSM Design and Verification MP4 Flash Slide
Flip-Flop Timing Parameters MP4 Flash Slide
Sequential Circuit Timing MP4 Flash Slide
One-Hot State Machines MP4 Flash Slide
Other Flip-Flop Types MP4 Flash Slide
Registers MP4 Flash Slide
Register Design MP4 Flash Slide
Intro to Complex FSMs MP4 Flash Slide
Complex FSMs MP4 Flash Slide
Pipelining MP4 Flash Slide
Serial Transfers MP4 Flash Slide
Registers with Shared Logic MP4 Flash Slide
Basic Processor Structure MP4 Flash Slide
Operation of a Basic Processor MP4 Flash Slide
Intro to Memory MP4 Flash Slide
SRAM Design MP4 Flash Slide
SRAM Arrays MP4 Flash Slide