此課程為數學研究的基礎﹐我們要談如何證明數學命題。參閱進度表

This course is the basis of mathematical research. We will talk about how to prove mathematical propositions. See schedule

0. 歐基里德的幾何原本
1. On Characterizations of the Gamma Function Math Mag,Vol.68, No.4, 1995.10,pp.301-305
2. 從尤拉數 e 到 Stirling 常數 數學傳播季刊, 中研院數學所出版,第20卷,第1期,1996.03,第34-45頁
3. 不等式中的伸縮因子 東海學報,第39卷,1998.07,第45-51頁
4. 用Mathematica對自然數次方和之探討 東海科學,第2卷,第 期,2000.07,第55-68頁
5. A Note on the Sums of Powers of Consecutive Integers 東海科學,Vol.5,2003.08,pp.101-106
6. 用Mathematica對自然數之負次方和的探討 東海科學,第5卷,第 期,2003.08,第61-75頁
7. 數論輕鬆遊 數學傳播季刊, 中研院數學所出版,第29卷,第4期,2005.12,第45-71頁
8. 傳統密碼之旅(上) 數學傳播季刊, 中研院數學所出版,第30卷,第1期,2006.03,第61-80頁
9. 傳統密碼之旅(下) 數學傳播季刊, 中研院數學所出版,第30卷,第2期,2006.06,第55-76頁
10. 交錯級數收斂性的探討 數學傳播季刊, 中研院數學所出版,第35卷,第3期,2011.09,第22-30頁
11. 「抽象代數」真的抽象嗎？(上) 數學傳播季刊,第36卷,第2期,2012.06,第34-51頁
12. 「抽象代數」真的抽象嗎？(下) 數學傳播季刊,第36卷,第3期,2012.09,第24-40頁
13. 從費馬到拉格蘭日 數學傳播季刊, 中研院數學所出版,第39卷,第1期,2015.03,第39-45頁

0. Euclid’s Elements
1. On Characterizations of the Gamma Function Math Mag,Vol.68, No.4, 1995.10,pp.301-305
2. From Euler's number e to Stirling's constant Mathematics Communication Quarterly, published by the Institute of Mathematics, Academia Sinica, Volume 20, Issue 1, 1996.03, Pages 34-45
3. Scaling factors in inequalities Journal of Donghai University, Volume 39, 1998.07, Pages 45-51
4. Use Mathematica to discuss the sum of powers of natural numbers. Donghai Science, Volume 2, Issue, 2000.07, Pages 55-68
5. A Note on the Sums of Powers of Consecutive Integers Donghai Science,Vol.5,2003.08,pp.101-106
6. Discussion on the sum of negative powers of natural numbers using Mathematica Donghai Science, Volume 5, Issue, 2003.08, Pages 61-75
7. Easy Tour of Number Theory Mathematics Communication Quarterly, published by the Institute of Mathematics, Academia Sinica, Volume 29, Issue 4, 2005.12, Pages 45-71
8. Journey to traditional cryptography (Part 1) Mathematics Communication Quarterly, published by the Institute of Mathematics, Academia Sinica, Volume 30, Issue 1, 2006.03, Pages 61-80
9. Journey to traditional cryptography (Part 2) Mathematics Communication Quarterly, published by the Institute of Mathematics, Academia Sinica, Volume 30, Issue 2, 2006.06, Pages 55-76
10. Discussion on the convergence of alternating series Mathematics Communication Quarterly, published by the Institute of Mathematics, Academia Sinica, Volume 35, Issue 3, 2011.09, Pages 22-30
11. Is "Abstract Algebra" really abstract? (Part 1) Mathematics Communication Quarterly, Volume 36, Issue 2, 2012.06, Pages 34-51
12. Is "Abstract Algebra" really abstract? (Part 2) Mathematics Communication Quarterly, Volume 36, Issue 3, 2012.09, Pages 24-40
13. From Fermat to Lagrange Mathematics Communication Quarterly, published by the Institute of Mathematics, Academia Sinica, Volume 39, Issue 1, 2015.03, Pages 39-45