The Soloist: The Movie

My viewing of “The Soloist” recalled how cruel Fate can be to nice people. It placed the homeless, especially the mentally ill ones, in my face and forced me to deal with this unfortunate reality. Then it ushered me a quick glimpse of the world of classical music. “The Soloist” spins both topics as subplots around a remake of the Joseph story in the Book of Genesis. Undoubtedly, this movie will vibrate the full range of your emotions. Now recall the Joseph story.

Joseph had a special gift.  Subject to a grip of jealousy, his brothers sold him into slavery. While in service, Joseph endured and emerged a powerful ruler. Years later, upon confronting his brothers he said:

“Don’t be afraid. Am I in the place of God? You intended to harm me, but God intended it for good to accomplish what is now being done, the saving of many lives.  So then, don’t be afraid. I will provide for you and your children.” And he reassured them and spoke kindly to them. Genesis 46:19-21

“The principal characters in this engaging movie are Nathaniel Ayers, played by Jamie Foxx, and Steve Lopez, played by Robert Downey Jr.  Ayers is a modern-day Joseph. Fate plays the composite characters of Joseph’s brothers who sells him into mental illness.

Like the Biblical Joseph, the young Ayers is a very talented person. To carve out a life as a musician, he abandons the distractions of his world, elevates the great composers to prophets of the god he seeks, masters their techniques thereby developing his musical talent, to earn enrollment in the famed Julliard School of Music. To continue click this link.

A Multiplication Algorithm

Is your child is having difficulty learning the multiplication algorithm or multiplication tables.  Has he mastered addition? If your answer to both questions is yes, place value may be his stumbling block. Good new! A simpler method exists. It is easy to learn …  Click this link to read more.

Three Elementary Counting Problems

Part I

Three counting problems
In how many ways can a photographer pose seven students in shoulder-to-shoulder alignment?

Two of the seven students adamantly refuse to be photographed side-by-side. In how many ways can a photographer pose the seven students respecting the students’ wishes?

The partners of a second couple announced they do not wish to be photographed side by side. If a photographer honors these two couples wishes, how many ways can the seven students be posed?

Prologue
This tutorial discusses the solution of three counting problems. The techniques discussed exposes secrets that are useful to solve many counting problems.

Are there formulas to remember? Yes! And they should be memorized!

But unlike your past mathematics experiences, substituting numbers into a formula is not the best method to solve counting problems.

A promising approach to solving counting problems is to break the given problem into simpler problems whose solutions lead to the solution of the more difficult given problem. Two fundamental counting principles are discussed. They are helpful in breaking a given problem into simpler problems for solution to the givnen problem.

The first of the two fundamental principles is the addition rule.

The addition rule
If there are m tags in an urn and n tags in a second urn then the total number of ways of selecting a tag from the first urn or the second urn is (m+n).

The second fundamental counting principle is a multiplicative rule, hence it is called the product rule.

Example: A student must select one book from the library’s collection of complexity theory or one book from l collection of Mozart’s biographies. The library has 5 books in its complexity collection and it has 20 biographies of Mozart. The addition rule asserts there are (5+20) ways to select a book from one of these two library collections.

To apply the addition rule,  for each complexity book, put its title on a tag and place the tag in an urn. Into a second urn, place a tag containing the name of each biography. The addition rule asserts that the total number of ways to select a book from the first collection or the second collection is (5+20).

The addition rule can be used in a different way. Consider this example.

Mary registered her upcoming wedding with Stacy Department Store. Stacy’s supplies 147 different plate designs of which 94 of the designs have non-circular plates. Mary likes only circular plates. How many choices does Mary have available through a Stacy’s registration?

In this example a tag describes a plate featured at Stacy’s. There are 94 tags identifying a non-circular plate. Denote by “n”, the number of Stacy’s circular plates. By the addition rule, 147=94+n. Hence, there are (147-94) circular plates available to Mary through a Stacy’s registration. The two urns are those containing the tags of circular plate designs and containing the tags of non-circular plate designs.

The product rule
If an urn contains m tags and a second urn contains n tags then there are m*n ways to form a list of two tags, where the first tag in the list comes from the first urn and the second tag in the list comes from the second urn.

A list is a presentation of objects along a line. Lists are ordered. They have a first object, a second object, etc.

Example:
Urn 1 contains three tags, each tag bearing one of the digit 1, 2, or 3.
Urn 2 contains two tags. One of the tags is marked “a” and the other tag is marked “b” .

The product rule asserts that there are 3*2=6 two-tagged lists, where the first tag is from Urn 1 and the second tag is from Urn 2.
The six lists are: 1a, 2a, 3a, 1b, 2b, 3b, 1c, 2c, 3c .

A Reminder: The product rule prescribes order within the lists. The first tag of the list is from the Urn 1 and the second tag of the list is from Urn 2. This ordering must be honored.

The above reminder asserts that 1c and c1 are different in that two-tagged list. In fact, c1 cannot occur from the order imposed in the construction of the list.

The two counting rules can be extended to more than two conditions (urns).

Example
Given three urns U1 having three tags, U2 having 4 tags, and U3 having 6 tags. No two urns share a tag. The number of ways of selecting a tag from U1 or U2 or U3 is (3+4+6)=13.

The Extended Addition Rule
Given k urns: U1, U2, …, Uk. U1 contains n1 tags, U2 contains n2 tags, …, and Uk contains nk tags such that no two urns share a tag then the total number of ways of selecting a tag from U1 or U2, …, or Uk is (n1+n2+…+nk).

Here n1 is used to represent the number of tags in the first urn. n2, n3, etc. is similarly defined.

The Extended Product Rule
Given k urns: U1, U2, …, Uk. U1 contains n1 tags, U2 contains n2 tags, …, and Uk contains nk tags then the total number of lists of length k with the first tag from U1, the second tag from U2, …, and the kth tag from Uk is the product n1*n2*…*nk.

Suggestion: Memorize the counting rules. A helpful strategy that aids memorizing the counting rules is to recite them to yourself each time you use them. They are the means through which a problem will be broken into smaller problems that leads to the solution to more complicated problems.

Problem 1: In how many ways can a photographer pose seven students in shoulder-to-shoulder alignment?

For the solution, follow this link.

A Black History Commemoration

(The polite terms of the period are used in this article.)

Fannie Lou Hamer, Martin Luther King, Jr., Thurgood Marshall, Madame C. J. Walker, W. E. B. DuBois, Booker T. Washington, Benjamin Bannecker, George Liele are all noteworthy selections that should be cited during Black History Month. Their accomplishments were stellar in the History of Americans of African descent. Their stories are inspiring. Their commitment and fortitude are noteworthy models to be used in future struggles against injustice.

Notwithstanding their noble accomplishments, this writing focuses on a sisterhood that spanned more than 90 years of American history. Its members are linked by their common choice to relinquish what little joy life may have offered, in order to enhance the lives of family members and friends. They were the washwomen of the Negro race in America. The times were the early days of the Negro’s struggle for dignity and freedom in the United States of America.

Carter G. Woodson first called attention to them in The Negro Washwoman, a Vanishing Figure. Venerable saints – he called them. Saints they were; seldom venerated; more often forgotten. This note retells their story and calls for an annual remembrance of their life-struggles – especially their progenies and disciples of compassion.

Their Story: Pre-Emancipation
Their story began in the South during the ante bellum era. They were in service to an often-truculent plantation mistress. Their jobs were to keep their mistresses’ lives free of drudgery. At dawn, they left their hut to prepare their mistress’ meals, to toil with their mistress’ children, to wash and iron their mistress’ household clothes and to clean their mistress’ houses, while their home went unattended until they returned at dusk.

Upon their return, they found their children craving  mother’s love and attention; and their tired husbands resting from the drudgeries of fieldwork and the indignities of their life-status. Without regard for self, these ladies launched into the second half of their day’s toil. But this time, they were cooking and caring for their loved ones, thereby, stoking the flame that fueled their raison d’etre.

The final task of her day our saint devoted to her home enterprise; washing clothes for pay. From whence springs the term, washwoman. With this income, she purchased presents and clothes for her family, and sometimes, household items that turned her hut into a home. Amidst servitude, to become a washwoman was to surrender self for the good of others. It was a life commitment to elevate her family from mere existing, to a life with occasional joy. Our saint ended her day with less than a six-hours rest, ever knowing, the next weekday promised a rerun of the same.

The ante bellum system was taxing to the slaves, but to the female slave it was most agonizing. Slave marriages were prohibited by law, so masters encouraged their female slaves “to take up” with a man. Absent love, she refused, but the master’s will prevailed. Some of these “unions” were lasting. But their purposes were to enlarge the master’s slave inventory for auction and maintenance of his slave force for service. This made birthing a child into slavery tortuous, but it made separating from that child to support such an economic system an agonizing abomination.

In the North the freed colored woman fared better. She did not have to contend with the problems of slavery. But her economic plight was no different. If her husband had no trade, he worked menial jobs for low pay. Many able wives without artistic talent opted to supplement their husband’s low wages by “taking in wash” for pay.

Their Story: Post-Emancipation
Emancipation changed everything. Black men withdrew their wives and daughters from the fields to work at home. Many former slaves migrated to the North to seek a better life. The defeated South was in economic disarray. Returning soldiers were granted the skilled jobs, leaving the menial jobs with less-than subsistence pay to the emancipated. This prevalent scenario forced emancipated females to supplement their family income. Without education or artistic skills, washing clothes in her home was the choice of many: the washwoman.

To many of the emancipated, the North promised more than it delivered. Recently freed males were highly skilled from their trade experience on plantations. Unions closed their rolls to the emancipated to protect their members from these highly skilled competitors, leaving for them menial jobs with very low pay. Freedom in the North had changed the slaves’ social status, but it failed to impact their economic viability.

In the North, the emancipated female did not have to contend with the command  “take up with a man” nor did she have to see her child on an auction block. But her family experienced economic hardship equal to that of her Southern counterpart.  For her life’s trials merely changed its face from the demanding mistress or the dictating master, to that of economic reality in a cruel world: a nonworking husband or one with low pay.

After emancipation, the washwomen continued their sacrifices over 90 years. Then demand for their services gave way to modern wash machinery, modern laundries, and a more educated black people. Their sacrifices and courage during times of stress provided the foundation for the descendants of slaves to build a life position that was more stable than one built on only financial injections to the family. From this foundation, the family was fortified spiritually, civically and educationally. For from the experiences of her home business, the washwoman learned the know-how that ushered the Negro people into forming business enterprises to serve their communities. From the wisdom she gained from observing the American society, she supported building and maintaining organizations through which many emerged into the mainstream. From her zeal to overcome societies’ inequities, she embraced education as the optimal delivery system to a better life for succeeding generations. To that end, she funded causes that fostered education and societies that fought for her community. But equally important, she upheld the primacy of male leadership within the family as a cornerstone of a strong family unit. Upon that rock, the Black family met and fought the war for civil rights in the ’60s.

To read more click the link. Call to Remember

The Winning Attitude for Learning Mathematics

Watching a group of children – ages one to three years, is very entertaining. The little ones celebrate their freedom from adult’s grasps by running, jumping, stooping and peeking through their fingers.

This is a fun time for them. They never sulk. They dash here and there; often so fast they fall on all fours. With exuberant giggles, they climb to their feet and run again, attempting to press the envelops of the new capabilities.  This is also a time for learning. With each activity, the little ones develop muscles to run faster, jump higher, stoop lower and observe more. Mastering these activities is fun. But it is hard work and it requires a lot of practice.

Jesus of Nazareth, one of the great teachers ever to live, used imagery of child behavior to describe how to excel in a spiritual life. In Matthew 18:1 – 4, Scripture records:

[1] At that time the disciples came to Jesus and asked, “Who is the greatest in the kingdom of heaven?”

[2] He called a little child and had him stand among them. 3 And he said: “I tell you the truth, unless you change and become like little children, you will never enter the kingdom of heaven.  4 Therefore, whoever humbles himself like this child is the greatest in the kingdom of heaven.

Paraphrasing the great teacher, those who attain greatness in a spiritual life must come with enthusiasm to master the new life skills. But more importantly, they must enter the new life unencumbered and be ready to meet its challenges.

Learning and a New Life
Learning opens us to a larger set of truth. The new knowledge (truths) offers a hope of better decision-making, thereby promising a chance for a better life. Effective use of our new knowledge takes us from our past life, with all its mistakes, into the new life of promise.

In Matthew 18:2-4, Jesus announced that one attained greatness in a spiritual life by having the attitude of a child. This winning attitude is characterized by enthusiasm to master the new life’s skills, freedom from encumbrances of the past and openness to new possibilities.

The model that Jesus used to explain gaining “ the kingdom of heaven” holds for gaining proficiency in mathematics. If one substitutes “learning mathematics” for the phrase “enter the kingdom of heaven”, the previous consequences continue to hold. Those who seek – in wonderment and astonishment, the laws of mathematics and push themselves to a deeper understanding of its nature, gain the proficiency (skills) of a mathematician.

Mathematics Teachers
Likewise, that analogue holds for teachers of mathematics. They, too, must have the same childlike attitude. For only a teacher with conceptual knowledge of basis skills can lead a student beyond rote learning to understanding. Such teachers have laid bare the secrets of what they teach. Therefore they are not likely to say
“… that’s the ways it is…” , or
“… you must do it this way…”  or
any other statement whose frequent use impairs a student eagerness to know, when seeking a clear explanation from a teacher who is not able to provide it.

Conclusion: The willing attitude for success in mathematics is the attitude of a young child. It is characterized by inquisitiveness and the drive to master tasks.

Kloosterman & et suggest the following to build motivation in the elementary classroom. Also they help nurture the willing attitude for learning mathematics. Assess their value towards helping your child’s mathematical development.  Click the link to continue

Gran Torino: The Movie

Clint Eastwood’s Gran Torino is a delight. It flashes humor in parts while it seriously tells the story of salvation of an American Hmong family.

Eastwood is a retired Ford Motor Company worker and a decorated veteran of the Korean War living in a Hmong neighborhood that was created by white flight.  Click to read more…

Internet Risks and Your Child

The second half of the 20th century brought the Internet into our homes. Unlike television, the Internet is a virtual center of human activity ready for us to  participate in with a few keystrokes on a computer.

Swiftly the Internet traffic grew and attracted our children.  They go to it on school computers, on homes computers, at their friends’ house, on library computers and even at grandma’s house. They took to the new media like fish take to water. It is no wonder; the Internet is dubbed their new playground.

Playgrounds are places where fun rules. And playground activities are rehearsals of valuable life skills. The Internet activities are no exception. They provide educational, social, and analytical skills training. Thus the Internet is too valuable an experience for a child not to be involved in its educational promises.

Risks of the Internet

The threat of physical danger is rare on the Internet. But this new playground does host a small element that spreads hatred, pornographic material, and seeks to commercially prey.

Our young ones are not always the prime targets of these nefarious activities. But during an unsupervised first encounter, an innocent child can easily be ensnared within these amoral webs.  Such an encounter may prove life altering.

Our objectives are to discuss some risks and dangers our children are likely to face on the Internet, and to offer suggestions to strengthen them against those dangers.

The Rewards of the Internet

The rewards of the Internet are many: Entertainment, instant communication, expression of one’s thoughts via web pages or through chat room participation, communication via email, visits to resources of cultural, scientific, and current importance; all with a few computer keystrokes.

Surveys document our children use the Internet responsibly. They do homework, communicate by email, text message, send instant messages, go to chat rooms, make scrapbooks, swap music, play games, construct games, create websites, write stories and some present content.

These activities develop social skills, analytical skills, and research and presentation techniques. All are desirable skills for the electronic age.

Internet: A Peril to Society, Our Defense

Despite the positive boasts of  the Internet, this media provides cover for a small population that takes advantage of the innocent; in particular the young. This cover is unwittingly provided by free access and the unsupervised nature of the Internet. It is through these attributes that the dangerous ideas and amoral activities are easily disseminated.

Disseminating views that are consonant with the public good is desirable. Those that are in dissonance with the public good must be countered. Society’s best defense against this dissonance is provided by parents who have pass their values and beliefs to their children before others can imprint them.

To read more, click this link.

The Original Flaky Pie Crust Recipe

There are culinary experiences that delights the senses. This is one of them, a flaky pie crust that is easy to prepare, tastes good, melts in your mouth and humbles the preparer as well as those enjoying it. Try it as written and check our claim.Click to read more

Create An Excitement For Mathematics: A Suggestion

Everyone does not have a passion to do mathematics. However an opened minded person can develop an appreciation for mathematics. This article advocates using writing exercises to develop interest in mathematics.

In the recent article, Write About Mathematicians In Non-Major Courses, appearing in the November 2008 MAA FOCUS, Professor Karl-Dieter Crisman reports the effects of requiring his students to write about people who do mathematics.

He reported students became interested in the person about whom they chose to write. Further some gained  helpful insights into their personal studies and formed a better attitude toward the mathematics.

In the words of the professor:

My experience is that essentially all students (often to my surprise) report that they learned something quite interesting about the individual they chose. … Most gratifying to me was that many students also seemed to gain real perspective about their own studies and future from learning about the challenges these real people faced in life, which promoted a better attitude toward mathematics in general by the end.

Recently I posted an article about Benjamin Bannecker. The intent of the article was to expose this self-taught mathematical talent to those who missed his story during their studies and readings. As I retraced Bannecker’s life, I felt I accompanied him while existing in a parallel world: observing the facts and stories of his life as they unfolded in my research.

In other words, Bannecker became a person to me. I felt I came to know him and I began to formulate his behavior and reactions to disputed things in his life. Often I found myself saying, “Bannecker wouldn’t do that.” And when he took bold political stances, I exhorted him with a “Right On Ben!“

As I learned more about Bannecker, my desire to understand his mathematical and scientific contributions grew. I dare say, I came to understand the effects of his moral, political, ethical and social life on his academic pursuits.

Professor Crisman observed a similar positive effect on his students’ attitudes. This effect suggests that writing about people who do mathematics can kindle appreciate for mathematics by identifying with its author.

Writing exercises are time consuming and keeping abreast of one’s school work leave little free time. Thus writing exercises are best undertaken during periods of light home assignments  – for instance during long vacations or summers.

The Assignment:
Write a three-page essay about a person who does mathematics. The essay should present some important facts about the person’s life and the student’s perspective about this individual. The students should support their feelings and further, highlight an application of his subject’s work.

Books to examine:

E. T. Bell   Men of Mathematics
H. Midonick   The Treasury if Mathematics
D. Campbell & J. C. Higgins  MATHEMATICS: People, Problems, Results
Also see the works of Dirk Struik and Howard Eves.

Professor Crisman presented the following categories to help choose a writing assignemnt.
(Old) Greek Mathematicians: Pappus, Archimedes, Apollonius, Euclid, Zeno, Democritus, Pythagoras

Female Mathematicians: Emmy Nether, Julia Robinson, Karen Hollenbeck, Karen Smith, Sophie Germaine, Fan Chung, Ingrid Dubieties, Florence Nightingale

Non-Western Mathematicians: Ramanujan, Al-Khwarizimi, Omar Khayyam, Lui Hui, Brahmagupta, G. Shimura, H. Hironaka, the Rhind Papyrus, Plimpton 322

Mathematicians who died young or violently or may have had mental illness: Nash (not deceased yet), Ramanujan, Riemann, Erdos, Boltzmann, Cantor, Galois, Abel

Mathematicians who thought (well or poorly) about God: Pascal, Descartes, Galileo, Laplace, Kronecker, Kepler, Russell, Hardy, Euler, Riemann, Ramanujan, Erdos, Cauchy

“Mathematicians” primarily known for something else: Pascal, Descartes, Mersenne, Galileo, Newton, Einstein, Pauli, Zeno, E. T. Bell, Stephen Wolfram, Charles Bell Jr., David Blackwell

Some influential 20 th century Mathematicians: David Blackwell, Von Neumann, Poincare, Emile Borel

For students who love to build models, consider assigning a three-page essay about Peaucellier’s Cell. The essay should introduce Captain Peaucellier and give an explanation of “the cell”, its importance and the writer’s perspective about Captain Peaucellier.

If a student finds no interests in the above suggestions, allow him to make his own writing choice.

Some useful websites:

http://www~groups.dcs.st~and.ac.uk;80/~history/
http://maathworld.wolfram.com

Home for the Holidays

Christmas is the time humanity unfurls to receive and to give. We open ourselves to music, laughter, kindness, love for others, social gatherings, good foods, and memories of past traditions.

Lucky are those who have a venue to enjoy these fruits of the holiday season. For others, this can be a stressful time.

In the Sacramento Valley we are blessed with an evolving tradition that provides a gathering to those who yearn the fruits of this season. Enjoyed with family, or friends, it’s truly electric and memorable.

Alone?

Come and bathe in the friendliness of the crowd.

Experience love through music, song, dance and story.  You’ll leave with a new excitement for life and new memories.

This Evolving Event is the holiday performance of the Sacramento Choral Society and Orchestra, “Home for the Holidays“.  Held in the beautiful Mondavi Center of  the University of California Davis on Saturday, December 13 at 2 PM, “Home for the Holidays” will prepare you for  “the days of Christmas” and reintroduce you to the beauty of the arts in the Sacramento Valley.

Come Home for the Holidays.