Sheracaolity

開課年度：105-2

授課教師：陳君明教授

開課系所與授課對象：數學系選修

私心推薦指數（滿分十分）：七分

課程大概內容

1. Introduction to Cryptography and Data Security
2. Stream Ciphers
3. The Data Encryption Standard (DES) and Alternatives
4. The Advanced Encryption Standard (AES)
5. More About Block Ciphers
Midterm
6. Introduction to Public-Key Cryptography
7. The RSA Cryptosystem
8. Public-Key Cryptosystems Based on the Discrete Logarithm Problem
9. Elliptic Curve Cryptosystems
10. Digital Signatures
11. Hash Functions
12. Message Authentication Codes (MACs)
13. Key Establishment Final

開課年度：105-2

授課教師：蔡忠潤教授

開課系所與授課對象：數學系必修，可抵其他微積分課

私心推薦指數（滿分十分）：九分

課程大概內容

1. Functions of several variables and continuity  2. Partial derivatives
3. Differential of a function
4. Chain rule
5. Mean value and Taylor theorem in several variables
6. Integral of functions with a parameter
7. Line integrals
8. The fundamental theorem on line integrals
Midterm 1  9. Implicit functions
10. Inverse function
11. Maxima and minima
12. Lagrange multiplier
13. Solving inverse map by iterations, Dependent functions
14. Area, double integrals and Integrals in higher dimensions
15. Change of variable formula
Midterm 2 
16. Improper multiple integrals
17. Integrals in curvilinear coordinates
18. Higher dimensional integrals
19. Improper integrals with a parameter
20. Green's theorem
21. Applications and interpretations by flows
22. Orientation of surfaces and surface integrals
23. Gauss's theorem in space
24. Stokes's theorem in space
25. Higher dimensions
Final