Math 147: PreCalculus

Professor:

Critical Competencies for Life

Here is a list of critical competencies for citizens and workers from leaders in business, industry, and government (Gardiner, 1994):

• Personal responsibility,
• Ability to act in principled, ethical fashion,
• Skill in oral and written communication,
• Interpersonal and team skills,
• Skills in critical thinking and problem-solving,
• Respect for people different from oneself,
• Ability to change,
• Ability and desire for lifelong learning.

Expectations for Math 147:

• working with functions: f(x)=___, then what is f(x+1).
• how do you graph it.
• what is the equation, what is f(x)+1, what is f(2x).
• what is f(t)? (needed for almost everything in the Signals & Transforms course).
• working with complex numbers: convert rectangular co-ordinates to polar co-ordinates and the reverse.
• plotting a number in the complex Cartesian plane regardless of the form.
• completing the square (needed for inverse transforms).
• graphing exponential functions: knowing y=exp(x) is an always positive function, that grows as x grows. exp(-x) is an always positive function that decreases to zero as x grows.
• working with inequalities: t-2<5, t+3>4, t+2>2 which t satisfy this? (needed for setting up convolution integral boundaries).
• working with absolute values: |x|<3 is which values of x? |x-1|<3 ?
• graph f(x)=exp(-|x|) (needed for many things).
• working with functions when the variable is not x.
• double angle, half angle formulas for sine, cosine.
• inverse trig functions.
• factor quadratics, quadratic formula.
• log, exp functions - properties, etc.
• Pythagorean identities.
• know (sin 2x)² is not sin² 4x² (it's (sin2x)*(sin2x) or sin²(2x)).
• parabolic shape, find vertex, where f(x) > 0, f(x) < 0.
• standard form of a circle.
• transformations; stretch, shrink.
• trig, exp, log equations.
• be good at algebra.

Boise State Univeristy Policies

• Boise State University's shared values.
• Boise State University's Student Conduct Home page

Helpful Course Material

Course Syllabus. A copy, in pdf format, of the syllabus handed out in class. Also available is the PowerPoint® course introduction shown in class.

Course Schedule. A copy, in pdf format, of the schedule from the syllabus.

The ALEKS list of topics is now on the web.

For your convenience, here is a link to ALEKS.

Online Graphing Calculator Manual. The manual for your graphing calculator can be accessed by following the link titled Graphing Calculator Manual with Exercises on the this web page.

Helpful Trigonometric Function Links

Here is an excellent link to help you understand trigonometric functions. From this page are other excellent links. Especially look at the Unit Circle in Trigonometry and sin(x), cos(x) and tan(x) link near the bottom of the page. This web page shows how the trigonometric functions are related to the unit circle. Check out the tutorial! Other good pages from the trigonometric functions web page are the sin(x), cos(x), etc. links. Once at these pages, click the tutorial button. These sites show the general form of the trigonometric functions and how changes to one of the parameters, a, b, c, d, change the shape of the plot of the trigomometic function.

Helpful Enrichment Links

The Cornell Method for Note-taking is a simple system for note-taking and organizing your notes. The link is to a pdf file. The method suggests that you use telegraphic sentences. I had to look this up. In their book How to Study for College, Pauk and Owens indicate that "[t]he best way to take notes is telegraphically. Long before e-mail and the fax machine were invented, important business and personal messages were sent by telegraph. The sender paid by the word; the fewer the words, the lower the cost. To save valuable time when you're taking notes, leave out unneccessary words such as articles (a, an, the), abbreviate words you use often, and streamline definitions by using a colon (:) or a dash (-)."

I found a web page that has the steps to problem solving recommended in the book How To Solve It: A new aspect of Mathematical Method by George Polya. The web page was written by Peter Alfeld, a math professor at the University of Utah. He has some other links on this web site that you might find helpful and interesting.

Academic Support Services at Boise State is provided to help you improve your chance at success at Boise State. They have tips on how to study, take notes, prepare for exams, take exams, etc. Academic Support Services is an excellent resource to improve learning skills and therefore enjoy Boise State more.

Learning to Learn. A paper in pdf format by Karl Wirth and Dexter Perkins that provides a summary of different learning styles and learning philosophies. The authors are geologists, but the paper discusses learning for a general audience. Click here for a direct link to the paper and other interesting materials.

Bloom's Taxonomy of Learning Styles. You might find it interesting to see the levels of knowledge proposed by Bloom, a seminal pioneer in learning styles.

Prof. Richard Felder is a Chemical Engineering Emeritus Professor at North Carolina State University. He is a highly regarded engineering professor who focuses on learning and engineering education.

• Student handouts from Dr. Felder's web page.
  • "How to Survive Engineering School." Success strategies for engineering students (and all other students).
  • Index of Learning Styles. Take this short survey to find your learning style.

Vark Guide to Learning Styles. Here is another survey to find your learning style.

Characteristics of a Successful Student from Cuesta College.

The Critical Thinking Community is an organization to help you learn how to think critically.

Helpful books for improving your learning skills

You may find the books Studying Engineering: A Road Map to a Rewarding Career by Raymond B. Landis (available from Discovery Press) or How To Study In College by Walter Pauk and Ross J. Q. Owens helpful.

Studying Engineering discusses the engineering profession and provides a lot of helpful information to succeed in your studies. The book also discusses the different types of engineering and provides information to help with your job search, either for summer employment or full-time work after graduation. I found this book informative about the engineering profession, study skills, and job searches.

How To Study In College is a basic book that discusses studying strategies for success in College. This book goes into more detail about studying, note-taking, and reading strategies than Studying Engineering. However, this book does not cover the engineering profession or job seeking skills. The book is aimed at a broader student audience.

A book aimed at problem solving is How To Solve It: A new aspect of Mathematical Method by George Polya. This book is highly regarded and often recommended to help improve your problem solving skills.

A book I found unexpectedly fascinating is Wins, Losses, and Lessons: An Autobiography by Lou Holtz, the retired football coach. This book is not really about football; it is about the importance of learning throughout life. When I started reading it, I thought it would be a rather poorly written, corny coach's memoir. I was surprised at how much I enjoyed the book and how much I learned from it. Some of the terms Holtz uses, like "learning how to learn" are the same terms as books on teaching use. Holtz is a strong proponent of life-long learning and taking advantage of opportunities.

Fun (?) stuff

Here are some articles about learning or math that you may find interesting. Read them if you wish in your spare time. Let me know what you think about them. Are they interesting? Worthwhile? Motivating?

• Abandoning Dead Ends: Embracing Lively Beginings. A paper in pdf format by Edward Burger and Michael Starbird. These two authors are recognized distinguished Mathemantics lecturers and this paper is a spoof on previous teaching practices in a funny, readable format.
• Pleasures vs. Problems. Another easy-to-read paper from Burger and Starbird.
• Last of the Metrozoids. A story about learning (and life) told through a group of young boys playing flag-football. Written by Adam Gopnik, an excellent writer. I really enjoyed this article and I thought the writing was incredible.
• An excellent book about creativity and what skills will be highly demanded in the workplace is A Whole New Mind: Why Right-Brainers Will Rule the Future by Daniel Pink. The right side of your brain is where "creative" activity occurs. The left side of your brain is the "analytical" side. A similar book is Tom Friedman's best selling book The World is Flat: A Brief History of the Twenty-first Century. Creativity can set you apart from your peers that are applying for the same jobs. Make yourself stand apart.
• Another excellent book is Einstein's Heroes: Imagining the World through the Language of Mathematics by Robyn Arianrhod. As the Library Journal writes, "An intriguing blend of science, history, and biography.... Arianrhod's well-written,fascinating discussion of intertwined topics not usually presented in one book aimed at general readers. Highly recommended."
• Another book I find fascinating is Wins, Losses, and Lessons: An Autobiography by Lou Holtz, the retired football coach. This book is not about football, but really about the importance of learning. Some of the terms Holtz uses, like "learning how to learn" are the same terms as books on teaching use.
• I think a great book to read for PreCalcuus is Descartes: The Life and Times of a Genius by A. C. Grayling. As you will figure out, the Cartesian Co-ordinate system is named for Descartes. The myth is that while lazing in bed starting at a fly crawling across the ceiling, Descartes developed the idea of a two-axis system to reference points in space.

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Last updated January 11, 2008 by William P. Clement.
© William P. Clement 2008