Personal Life-Understanding Math and Science (PLUMS) 施天谟 （ Tien-Mo Shih ） (Tim)

1. 教育科研的最终目的是让人们享有安详丰富的生命和生活。教育科研的最终目的是让人们享有安详丰富的生命和生活。 The ultimate goal of education and research is to enrich life and promote peace. Personal Life-Understanding Math and Science (PLUMS) 施天谟（Tien-Mo Shih）(Tim) Department of Physics, Xiamen University

2. Purpose of Education Not just to help students to find jobs

3. Personal-Life Understanding Math Sciences (PLUMS)

4. Outline • Motivation of PLUMS Course (Life, Life, Life) • What is PLUMS? • Benefits of PLUMS • Website and Examples • Questions + Interactions • Small Exercises

5. Motivation • Give us a different perspective regarding a learning process (taking a course, education)

6. Gaining Knowledge ?? • When do we start producing?

7. Gold Mine in Our Backyard

8. Brian Cells （脑细胞） • Most of people have not ever used 90% of their brain neural cells when they die. • Thinking stimulates growth of brain cells • Brain exercises are similar to body exercises

9. To Both of Us and Society • Something beneficial, familiar, and interesting ???

10. Beneficial • How to cure cancers? How to reduce hurricanes? • But there are more specialized journal papers.

11. Familiar? • Swimming? Dancing? Our Neighbors? Political Views?

12. About Everyday Life Nursing Home Visits

13. Definition of “PLUMS” • Personal Life-Understanding Math and Sciences • Identify personal daily-life-related issues • Transform thoughts into text words • Model them into equations • Compute them with MATLAB to produce numbers • 美国有苹果；中国有李子。

14. Repeat Thoughts Words Equations Numbers 4 states, 3 processes

15. Examples of PLUMS Topics • 较严肃的理工数 课题 (STEM) • 古典的中国舞蹈 (Classical Chinese Dance) • 减肥 (Weight Loss) • 我们人生的目标 (How to best live our lives)

16. Recommendations for PLUMS Essay Writing • Clear (20%) • Interesting (entertaining) (20%) • Frank, individualistic, non-八股文 (20%) (our own, our own, our own) • Persisting (self-disciplining) (20%) (2 pages per week) • Modeling and numbers (20%)

17. What is so great about numbers? • Numbers = Civilization

18. STEM (理工数）

19. BioChemMedical (生化医)

20. A Viewpoint • 35 years of teaching/research experiences at UMCP, XMU • C-grade teachers for Linear Algebra （线性代数）[A]{x} = {b} • B-grade teachers give examples 3x + 4y = 7, 5x – 4y = 1 • A-grade teachers give life-related examples （鸡兔同笼） chicken and rabbits in a cage c + r = 7, 2*c + 4*r = 22

21. 100 Thousand Why’s • Why can we ice-skate on ice, but not on dry ice? • Why is the sky blue? • Why, why, why?

22. Modeling 都市计划 • City 1 (1 million) 2? 3? City4 (200K) ( p2 – p2_old)/ dt = c1*(p1 – p2) – c1*(p2 – p3) + c2*p2 increase of population at city2 = in – out + net birth

23. Modeling 爱情 (II) • (p – pp ) /Δt = - c1 * p or p = pp / (1 + c1*Δt) p: passion (激情） pp: past passion (一个月前的激情）

24. 激情是时间的函数Passion 有了交流，也许爱情就持续下去了。 P and C coupled

25. Modeling Procedures • Mass conservation • Momentum conservation (linear and angular) • Energy conservation • Constituent equations • Author self-assumed principles • 3 steps: (1) identify principles, (2) introduce symbols and constituent relationships (3) set up equations according to (1) and (2).

26. Monte Carlo Method • clc; clear • n=0; nc=1000000; • for count=1:nc • a=rand(2); • s=a(1,1)^2+a(2,2)^2; if(s <=1); n=n+1; end • end • pimc=4*n/nc ( π = 3.1416 ) More modeling techniques are described in Appendix.

27. More Convincing （松弛法） • x^4 - 0.5 x – 15 = 0 A solution, x = 2, exists. • % x^4 = xb^3 * x • clc; clear; • xb=4; ga=0.25; % initial guess • for iter=1:20 • x = ga*(0.5*xb + 15)/xb^3 +(1-ga)*xb; • xb=x; • fprintf('%5.0f %9.4f \n', iter, x) • end

28. Abrupt Changes (Ga = 1) • 1 0.2656 • 2 807.4447 • 3 0.0000 • 4 29807672274199790000.0000 • 5 0.0000 • 6 84168506673636771000000000000000.0000 • 7 0.0000 • 8 Inf • 9 Inf • 10 Inf (解答发散了）

29. Gradual Changes (ga = 0.25) • 1 3.0664 • 2 2.4432 • 3 2.1105 • 4 2.0098 • 5 2.0002 • 6 2.0000 • 7 2.0000 • 8 2.0000 • 9 2.0000 （解答收敛了） • 10 2.0000

30. More Convincing (可信度高) • x + y + z = 3 • x – y + z = 1 • x + y – z = 1

31. Messy Room（乱糟糟）

32. Jumping into Swimming Pool

33. To Run for the President(稳扎稳打)

34. Climb the Mountain（爬山）

35. 慢慢来，胜率高 

36. Easier for Us to Understand • Yesterday I jogged for a long distance. • Yesterday I jogged for 10 km. • There were many attendees in the party. • There were about 200 attendees in theparty. • 昨天的party有很多人参加 • 昨天的party 有两百多人参加

37. Easier for Us to Explore (探索） • About a century ago, the 2nd law of thermodynamics did not exist. （热力学第二定律） • Human beings only knew that energy could not transfer from a cold body to a hot body. • Carnot invented Carnot engine. • Entropy , s = 7.354 kJ/kg-K at T=100C, and p = 1 atm for steam • 逐渐地，熵出现了

38. Numbers and Thinking Ability • Independent Thinking Ability (ITA) 独立思考能力 the most pronounced trait of successful people, for example, Bill Gates, Steve Jobs, Martin Luther • Logical Thinking Ability (LoTA) 逻辑思考能力 Hanoi Tower （n = 64) 18446744073709551615/31556952 秒= 584554049253.855年 • Creative Thinking Ability (CreTA) 想像力 1378 59 246

39. Writing Ability • Clarity (ability to express oneself) • Fluency • Rigorousness (严谨） Thank you for your photos  Thank you for taking photos for me and sending them to me • Logic

40. Techniques of Building PLUMSEssays • Darting Method (胡思乱想法） 道可道，非常道  honesty  not hurting others’ feelings  short run, long run?  face lift, eye-corner deposit  no capacity  NHV  criticism = hostility  Joe, grandson, and donkey  LWOPO, not LFOPO • Inquiry Method (自问自答法） • Definition Method（定义法） • Combination of the three methods

41. MATLAB • Install MATLAB Software Package in your own PC

42. PLUMS Website • http://phys.xmu.edu.cn/plums • Given a journal paper ID when accepted.

43. Entrepreneurship 中国创业的大学毕业生会增多

44. About Tien-Mo (Tim) Shih (施天谟) • Research & Teaching ≈ 35 years • Professor, Department of Physics, Xiamen University • Education: UC Berkeley (Ph. D.); Harvard (postdoctoral fellow) • Authored two books: “Numerical Heat Transfer” “Heat Transfer” • Hurricanes and typhoons • Vegetarian • Heath, Conscience, Love, Career • tmshih@xmu.edu.cn

45. Questions? Comments?

46. Appendix – Examples of Modeling Techniques • 1. Genetic ChartAlmost all sentences we write in an essay can be categorized into facts (or factual statements) in successive generations. Facts in the nth generation are descendents of those in (n-1)th or even older, and are ancestors of those in (n+1)th or younger. Realizing this phenomenon and knowing how to construct such charts will help us to cultivate our LoTA.

47. F1a = We study together in Xiamen University.F1b = Xiamen University is situated in China.F1c = Students who have studied together on the same campus are called alumni after graduation.F2a = We study together in China.F2b = We will be alumni after graduation and forever. Hence, F1a + F1b  F2a; F1a + F1c  F2b.

48. Description: A farmer plans to bring a dog, a chicken, and a bag of rice from the left bank of the river to the right bank of the river, as shown. Constraints (or facts): (a) A boat allows him to bring not more than one item at a time (zero is OK). (b) As long as he is around and on guard, everything is peaceful.(c) As soon as he is not around, dog will eat chicken, or chicken will eat rice.

49. Objectives: • (a) How does the farmer safely bring all 3 items from bank a to bank c? • (b) Most importantly, how can we model this logical puzzle into a math problem, so that we can use MATLAB to compute it?

50. clc; clear • % f=farmer; d=dog; c=chicken; r=rice; • % a: left bank; b: at the middle of the river; c: right bank • % 3 constraints: • % (1) St = 17 for all time steps. • % (2) Sb cannot exceed 14 for all time steps. • % (3) Sa, Sb, or Sc cannot be equal to 3 or 6 for all time steps. • % at t=0; Sa=17; Sb=0; Sc=0; • f=10; d=4; c=2; r=1; • Sa(1)=f + d + c + r; Sb(1)=0; Sc(1)=0; % at t=0; • Sa(2)=Sa(1)-f-c; Sb(2)=Sb(1)+f+c; Sc(2)=Sc(1); • Sa(3)=Sa(2); Sb(3)=Sb(2)-f-c; Sc(3)=Sc(2)+f+c; • Sa(4)=Sa(3); Sb(4)=Sb(3)+f; Sc(4)=Sc(3)-f; • Sa(5)=Sa(4)+f; Sb(5)=Sb(4)-f; Sc(5)=Sc(4); • Sa(6)=Sa(5)-f-d; Sb(6)=Sb(5)+f+d; Sc(6)=Sc(5); • Sa(7)=Sa(6); Sb(7)=Sb(6)-f-d; Sc(7)=Sc(6)+f+d; • Sa(8)=Sa(7); Sb(8)=Sb(7)+f+c; Sc(8)=Sc(7)-f-c;