离散数学-ch1-Introduction

文章目录

1. Overview
- Grading Breakdown
- Faculty Information
- 网站
- Three Parts of CDM(*)
- Textbooks
- 移位运算符
- 位运算符与（&）运算符异或^
- question
- 本课词汇

1. Overview

References

• Stanford CS103, https://web.stanford.edu/class/cs103

• NYU G22.2390-001, https://cvc4.cs.stanford.edu/logic/ • CMU CDM http://www.cs.cmu.edu/~cdm/

• UB CS70 http://inst.eecs.berkeley.edu/~cs70/fa16/
• CMU-CS122 https://www.cs.cmu.edu/~iliano/courses/17F-CMU-CS122/

• Stanford CS103, https://web.stanford.edu/class/cs103

• CMU 15-453 https://www.cs.cmu.edu/~fp/courses/flac/
• Columbia, COMS W3261, http://www.cs.columbia.edu/~aho/cs3261/ • IITJodhpur,CS222,http://krchowdhary.com/toc/cs222.html
• 南京大学离散数学课程

To Be Distinguished, You Need To

Take

✓ Lectures
✓ Recitation (Optional)

Do
✓ 3 Labs
✓ Preliminary Questions
✓ Homework

Pass
✓ Quiz

✓ Finalexam

Grading Breakdown

Others 20%
Lab 20%
Quiz 20%
Final 40%

Faculty Information

网站

Website:

http://ipads.se.sjtu.edu.cn/courses/cdm

Canvas:

https://oc.sjtu.edu.cn/courses/24410

形式化验证网站：

https://rise4fun.com/Dafny/tutorial

Three Parts of CDM(*)

Part I. Reasoning. (8 ~ 9 Weeks)

How to prove the correctness?

Part II. Computability. (~ 6 Weeks)
Is the problem computable (solvable)?

Part III. Probability. (~1 Weeks)

How does computer solve continuous problem? (Underneath the ML)

Textbooks

《数理逻辑与集合论》第2版 • 石纯一著，清华大学出版社

John E. Hopcroft, Rajeev Motwani and Jeffrey D. Ullman, Introduction to Automata Theory, Languages, and Computation, Pearson, 2001

移位运算符

左移（<<）

i = i << n ; 相当于 i = i * (2 ^ n )

右移（>>）

i = i >> n ; 相当于 i = i / ( 2 ^ n )

位运算符与（&）运算符异或^

位操作中的与操作运算符。也就是常说的and操作，双目运算符。
计算的时候按位计算，&两边操作数对应位上全为1时，结果的该位值为1。否则该位值为0
比如0x12&0x23 转为二进制为:B00010010&B00100011，按位计算结果为B00000010，
即结果为0x02

两个二进制操作数对应位相同为0，不同为1;

异或交换取值

void swap(int a, int b)
{a ^= b;b ^= a; a ^= b;
}

参考：

https://blog.csdn.net/mofeigege/article/details/106304076?ops_request_misc=%257B%2522request%255Fid%2522%253A%2522159995841819725222400123%2522%252C%2522scm%2522%253A%252220140713.130102334…%2522%257D&request_id=159995841819725222400123&biz_id=0&utm_medium=distribute.pc_search_result.none-task-blog-2_alltop_click~default-1-106304076.first_rank_ecpm_v3_pc_rank_v2&utm_term=位运算符&spm=1018.2118.3001.4187

https://jingyan.baidu.com/article/a3f121e4919494fc9052bb0f.html

question

Three Parts of CDM CDM：computer Discrete Mathematics? Yes

(Underneath the ML):Machine Learning? Yes

形式化验证举例：

method clone(n: nat) returns (b : nat)
ensures b == n
{
var i := 0;
while i < n
invariant 0 <= i && i <= n
{
i := i + 1;
}
return i; }

本课词汇

1.Propositional 命题

2.semantic 语义的