Personal Life-Understanding Math and Science (PLUMS)

施天谟（ Tien-Mo Shih ） (Tim)

Department of Physics, Xiamen University

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.

Purpose of Education

Not just to help students to find jobs

Personal-Life Understanding Math Sciences (PLUMS)

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

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

Gaining Knowledge ??When do we start producing?

Gold Mine in Our Backyard

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

To Both of Us and SocietySomething beneficial, familiar, and

interesting

???

BeneficialHow to cure cancers? How to reduce

hurricanes? But there are more specialized journal

papers.

Familiar?Swimming? Dancing? Our Neighbors?

Political Views?

About Everyday Life

Nursing Home Visits

Definition of “PLUMS”Personal Life-Understanding Math and Sciences Identify personal daily-life-related issuesTransform thoughts into text words Model them into equationsCompute them with MATLAB to produce numbers

美国有苹果；中国有李子。

RepeatThoughts Words Equations

Numbers 4 states, 3 processes

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)

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%)

What is so great about numbers?

Numbers = Civilization

STEM ( 理工数）

BioChemMedical ( 生化医 )

A Viewpoint35 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 = 1A-grade teachers give life-related examples （鸡兔同笼） chicken and rabbits in a cage c + r = 7, 2*c + 4*r = 22

100 Thousand Why’sWhy can we ice-skate on ice, but not on dry

ice?Why is the sky blue? Why, why, why?

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

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）

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

Modeling ProceduresMass conservationMomentum conservation (linear and angular)Energy conservationConstituent equationsAuthor self-assumed principles3 steps: (1) identify principles, (2) introduce symbols and constituent relationships (3) set up equations according to (1) and (2).

Monte Carlo Methodclc; clearn=0; nc=1000000;for count=1:nca=rand(2);s=a(1,1)^2+a(2,2)^2; if(s <=1); n=n+1; end endpimc=4*n/nc ( π = 3.1416 )

More modeling techniques are described in Appendix.

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

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）

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

More Convincing ( 可信度高 )

x + y + z = 3

x – y + z = 1x + y – z = 1

Messy Room （乱糟糟）

Jumping into Swimming Pool

To Run for the President( 稳扎稳打 )

Climb the Mountain （爬山）

慢慢来，胜率高

Easier for Us to UnderstandYesterday 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 the

party.

昨天的 party 有很多人参加昨天的 party 有两百多人参加

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

Numbers and Thinking AbilityIndependent 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

Writing AbilityClarity (ability to express oneself)Fluency Rigorousness ( 严谨） Thank you for your photos Thank you for

taking photos for me and sending them to meLogic

Techniques of Building PLUMS EssaysDarting 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

MATLAB• Install MATLAB Software Package in your own PC

PLUMS Websitehttp://phys.xmu.edu.cn/plumsGiven a journal paper ID when accepted.

Entrepreneurship 中国创业的大学毕业生会增多

About Tien-Mo (Tim) Shih ( 施天谟 )

Research & Teaching ≈ 35 yearsProfessor, 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

Questions? Comments?

1. Genetic Chart

Almost 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.

Appendix – Examples of Modeling Techniques

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.

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.

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?

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;

Sa(9)=Sa(8)+f+c; Sb(9)=Sb(8)-f-c; Sc(9)=Sc(8); Sa(10)=Sa(9)-f-r; Sb(10)=Sb(9)+f+r; Sc(10)=Sc(9); Sa(11)=Sa(10); Sb(11)=Sb(10)-f-r; Sc(11)=Sc(10)+f+r; Sa(12)=Sa(11); Sb(12)=Sb(11)+f; Sc(12)=Sc(11)-f; Sa(13)=Sa(12)+f; Sb(13)=Sb(12)-f; Sc(13)=Sc(12); Sa(14)=Sa(13)-f-c; Sb(14)=Sb(13)+f+c; Sc(14)=Sc(13); Sa(15)=Sa(14); Sb(15)=Sb(14)-f-c; Sc(15)=Sc(14)+f+c; % at t=14th hr for i=1:15 St(i)=Sa(i)+Sb(i)+Sc(i); end St Sa Sb Sc % at t = 15th hour, Sa=0; Sb=0; Sc=17; a successful task!

t = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 (time) St = 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 (total ) Sa = 17 5 5 5 15 1 1 1 13 2 2 2 12 0 0 Sb = 0 12 0 10 0 14 0 12 0 11 0 10 0 12 0 Sc = 0 0 12 2 2 2 16 4 4 4 15 5 5 5 17

F1a: dog eats chickenF1b: chicken eats riceF1c: dog is not interested in riceF1d: farmer can take only one item or go empty- handed at a time

F2: take the chickenF3: return bank (a) empty-handedF4: take the dogF5: return to bank (a) with the chickenF6: take the riceF7: return empty-handedF8: take the chicken

Life--Nonlinear Equations ( 非线性）

Success = function of (effort, vision, network, luck, …)

Happiness = function of (success, mentality, deeds, …)

努力一定成功吗？ 成功一定快乐吗？

Challenging ( 挑战性）

No Solution ( 没有解答） x y = 1

(x + 1) ^2 + (y – 1)^2 = 0.25

Obscure Locations ( 隐蔽处）The root lies in the valley.

Time Consuming ( 费时）Origin of Hurricane

1000 nodes in x, 1000 nodes in y, 1000 nodes in z.

u, v, w, p, ρ, T, moisture, turbulence~ 1 billion to 10 billion unknowns Mostly solving full matrices Let applied mathematicians worry