Monthly Archives: October 2005

Back to the Mission Statement

WARNING: This is a fairly long post. And my apologies to anyone who received multiple notices, I kept accidentally posting, prematurely.

It is a continuation of an earlier post, Mission Statement. In that post, as well as this one, I am attempting to set a direction for my life. The problem is that as of May this year, my family goals (at least of having one), my education goals and my career goals had been met. So, the question is, where do I go from here. There are obvious responsibilities that come with my present position in life, such as leading my family and performing on the job, but much more generally, “what is my life to accomplish and what does God have as a plan for my life and my family’s future?”

To start with I am developing a mission statement or a vision statement for my life over then next ten years. My goals will all be directly stemming from that vision. Here was the first draft as of the last posting on this topic:

I live my life in fellowship with Christ to draw others to him and to minister to those around me. I am a husband, a father, and a mathematician. My life is lived to serve others with the gifts that God has given me.

Since my goal is not brevity but completeness, I would like to expand it. Let me identify the necessary components of the vision statement at this point:

  1. My relationship with God
    • His priority over all else.
    • My dedication to follow his plan for my life and fully confessing that I believe he has a plan for me
    • Everything in my mission statement is done out of my devotion to Him.
    • My involvement in the development of my own faith as well as the faith of others, both in evangelism and discipleship.
    • Church fellowship and worship.
  2. My role as a husband to honor my wife and lead my family, spiritually.
  3. My role as a father to raise my children to love the Lord and follow his commands.
  4. My role as an educator, both to pass on lessons in mathematics but also to live a role model for integrating faith in daily life and to minister to students needs beyond the classroom.
  5. My role as a mathematics researcher, to further the development of my own intellect through the development of areas in Applied Mathematics, such as finite elements, curve fitting and stochastic modeling.
  6. Enjoyment of the life God has given me, through my hobbies and research and just playing with my family.

Now, consider the following edits:

Above all else, I live my life in fellowship with Christ. I know that God has a plan for my life and I seek to follow that plan. I live to draw others to him, to aid in the development of the faith of my brothers and sisters in Christ through a New Testament Church, and to minister to those around me. I am a as a husband, a father, an educator, and a mathematician. My life is lived to serve others with the gifts that God has given me.

  1. As a husband, I will honor my wife and lead my family, spiritually.
  2. As a father, I will raise my children to love the Lord and follow his commands.
  3. As an educator, I will teach mathematics with passion, live as a role model for integrating faith in daily life and minister to students’ needs beyond the classroom
  4. As a mathematician, I will further the development of my own intellect through the development of areas in Applied Mathematics, such as finite elements, curve fitting and stochastic modeling.

When it does not conflict with the above responsibilities, I will enjoy life through playtime.

I’ll chew on that for a while, but it looks pretty good to me. I am doing this publicly because I hope that anyone that reads this will feel free to point out things that might seem a bit out of place or anything I might have left out. I also recommend this as a good practice for anyone who is wondering what God’s will is. It is to develop an idea of what God’s vision is for your life. Answer the questions, “When you boil it all down to the bare essentials, who are you in God’s eyes?” And realize that is much more specific than we might first expect, after all, he knit us together in our mother’s womb, with a specific design in mind.

It might seem that for me to develop these plans is like the fool who built larger barns to house all his grain and then the next day his life was demanded from him. I view it much more in line with the servant who was given some of the master’s money (talents) and when the master returned, there was an accounting of what the servant had done with the master’s possessions. I am attempting to be a good steward of those talents and I hope that by laying out this vision, and ultimately the goals that follow, I may be found faithful when it is all said and done.

I’m done preaching, now. Sorry for seeming to get on my soapbox, but I am really preaching at myself so I’ll remember all this later on.

Blink Blink

I was posed a question:

What are the odds that in the span of the one eighth of a second it takes for a camera shutter to open and close, 18 people will all have their eyes open at the same time?

ANSWER: Assuming a blink rate of 20 blinks per min with an average blink duration of \frac{1}{4} second, the probability is 12.2%, or roughly 7 to 1 against. If the people make a reasonable effort to keep their eyes open, they may affect their blink rate. As an example, if the average blink rate can be subdued to a mere 4.75 blinks per minute, the probability rises to 59%, or roughly 1.4 to 1 in favor.

METHOD: In order to solve this problem, I accepted that the human eye blinking is a Poisson Process thus distributed according to the Poisson Distribution. In other words, if we let the average number of blinks over some interval of time be given by \lambda, then the probability of x blinks occuring over that interval is given by

\displaystyle P(x) = \frac{\lambda^x e^{-\lambda}}{x!}

Now, because the shutter is open for only \frac{1}{8} of a second and a blink will last \frac{1}{4} of a second, then if an individual blinks anywhere from \frac{1}{4} of a second before the shutter opens to when the shutter closes, they will appear to have their eyes closed in the picture. So we are look at an interval of \frac{1}{4}+\frac{1}{8} = \frac{3}{8}. Thus,

\displaystyle \lambda =\left( 20 \mbox{ blinks per second } \right) \left( 60 \mbox{ sec. per min. } \right) \left(\frac{3}{8} \mbox{ sec.} \right) = \frac{1}{8}

Therefore the probability that a single person’s eyes will be closed is\displaystyle P(1) = \frac{1}{8} e^{-1/8} \approx 0.1103. Thus the probability that their eyes are open will be 1-P(1) \approx 0.8897. Assuming independence among our 18 (no one person blinking affects another person’s blinking), the probability of all 18 having their eyes open will be (0.8897)^{18} \approx 0.122 = 12.2%.

If we repeat this process changing only the 20 blinks per minute to 4.75 blinks per minute, we obtain 59%.

——

Now wasn’t that special. HT: jonboy, for the question.

Any more questions, fire away in the comments or send me an email. I love to be distracted from actual work I need to be doing.

Back to normalcy

The downside to the first world series coming to Texas (other than the Astros’ losing) has been the late nights. Being only an occasional sports fan, I usually watch only the big games and usually only when they involve one of my teams. So, at least one nice thing can come out of the this travesty. We’ll be going to bed at a normal hour tomorrow.

A mathematician’s reading list

On my reading list page, I am keeping up with books I am reading, have read and intend to read. When I set it up, I realized that very there were none on my list related to my specific career choice, namely, a mathematician and a mathematic educator. I came across an article in this month’s Notices of the American Mathematical Society. The article that caught my eye was “The Mathematics Autodidact’s Aid” by Kristine K. Fowler. In it, she proposes some essential texts for various fields in mathematics. I have often wondered where to start if I wanted to introduce myself to various areas of research in mathematics, particularly in areas that I have had little or no background. I am appending my reading list with the following titles. I have put an asterisk next to ones I particularly am interested in, while the others are still worth listing but not as enticing.

Mathematics Reading

Writing and Researching

  • *Handbook of Writing for the Mathematical Sciences, Higham
  • *(Article) “Tools and Strategies for searching the research literature,” Molly T. White

History of Mathematics

  • *Concise History of Mathematics, Struik
  • *Math through the ages, Berlinghoff and Gouvea
  • History of Mathematics: An Introduction, Katz
  • Norton History of Mathematical Sciences: The Rainbow of Mathematics, Grattan-Guinness
  • The Companion Encylcopedia of the History and Philosophy of the Mathematical Sciences, Grattan-Guiness

Real Analysis

  • Advanced Calculus, Buck
  • Mathematical Analysis, Apostol
  • Introduction to Topology and Modern Analysis, Simmons
  • *Real Analysis: Modern Techniques and Their Applications, Folland
  • *Real Analysis, Royden.
  • *Selected Problems in Real Analysis, Makarov et al.

Ordinary and Partial Differential Equations

  • *Elementray Differential Equations and Boundary Value Problems, Boyce and Diprima
  • *Differential Equations, Dynamical Systems and an Introduction to Chaos by Hirsch, Smale and Devaney
  • Theory of Ordinary Differential Equations by Coddington and Levinson
  • Ordinary Differential Equations with Applications, Chicone
  • First Course in Partial Differential Equations with Complex Variables and Transform Methods, Weinberger
  • *Partial Differential Equations: An Introduction, Strauss
  • *Navier-Stokes Equations: Theory and Numerical Analysis, Temam’s

Numerical Analysis

  • *Numerical Mathematics, Quarteroni, Sacco and Saleri
  • *Matrix Computations, Golub and Van Loan
  • First Course in the Numerical Analysis of Differential Equations, Iserles’s
  • *Theoretical Numerical Analysis, Atkinson and Han (Functional Analysis framework)
  • *Handbook of Numerical Analysis, Ciarlet and Lions
  • Iterative Methods of Lienar and Nonlinear equations, Numerical Optimization, Nocedal and Wright
  • Numerical Initial Value Problems in Ordinary Differential Equations, Gear
  • Numerical Solution of Boundary Value Problems for Ordinary Differential Equations by Ascher, Matthejj and Russell
  • Finite Elements, Braess
  • *Numerical Approximation of Partial Differential Equations, Qarteroni and Vallil

Mathematics Education

  • International Handbook of Mathematics Education, Bishop
  • Handbook of Internation Researchi n Mathematics Education, English
  • Handbook of Research on Mathematics Teaching and Learning, Grouws
  • Handbook of Research Design in Science and Mathematics Education, Kelly and Lesh.

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Higher Dimensions

In teaching multi-variable Calculus, it is often a challenge to get students to begin to think beyond the 3 spatial dimensions. To illustrate the challenge, I often draw a four dimensional cube on the board and explain the difficulty in visualizing hyper-spatial volumes:


4 Dimensional Hyper-cube

We can actually easily get up to 5 dimensions in visualizations by using the three spatial dimensions, time (animation) and coloring. In fact, I used a piece of software to visualize output from weather simulations and it was called Viz5d (from the idea of visualizing 5 dimensional data).

I point all this out because I thought of it as I read the following article:

At Penn State University the mathematics department recently unveiled a new sculpture designed by mathematician, Adrian Ocneanu. The sculpture represents a 4-dimensional space in six cubic feet of 3-dimensional space. The article offers a compelling description of how the sculpture has turned out. Ocneanu himself says, “When I saw the actual sculpture, I had quite a shock…I never imagined the play of light on the surfaces. There are subtle optical effects that you can feel but can’t quite put your finger on.”

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Harriet Miers can’t be so bad

I am almost afraid to post this because I don’t want to get into a big political debate on this blog but I thought I ought to report on a fairly interesting finding. I was perusing the Harriet Miers nomination and looked over her biography. I never could put my finger on it but there was just something that I liked about her, and until now I just assumed it was my tendency to react against elitism or route for an underdog. No, it runs deeper than that: A Math Major on the Supreme Court!!

Check out her biography at Washington Post

She received a B.S. Degree with a Math Major from SMU in 1967.

How about that?

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