Wednesday, April 20, 2016

Wallis's formula for integrals of powers of sine and cosine

Please note that Wallis's formula is for definite integrals from 0 to π/2. You'll need to adjust the results for other intervals of integration (and for odd powers, for some intervals, you'll get zero because results in different quadrants cancel each other).

Friday, December 18, 2015

Frequently asked questions about Math 129

Q. What is Math 129?

A. Math 129 is an accelerated one-semester course that covers the entire algebra curriculum through the level of intermediate algebra. It contains the entire course content of Math 100 (Elementary Algebra) and Math 120 (Intermediate Algebra) and satisfies the prerequisite for any course with an intermediate algebra prerequisite.

Q. Who should take Math 129?

A. Math 129 is designed for exceptionally well-prepared students who can commit to two hours of math in class, five days a week, for an entire sixteen-week semester (plus many additional hours of work outside of class). Successful completion of Math 129 moves you rapidly through the math curriculum and accelerates your access to all of the courses that require algebra. Math 129 is also a good choice for students who previously did well in algebra but are re-entry students who have been away from school for several years and need a comprehensive algebra review.

Q. What is the format of Math 129?

A. Math 129 is a lecture course that meets Monday through Friday from 9:00 till 10:50 (with a 10-minute break). Many in-class quizzes are given; most of them are individual but a few are done as group work. Exams occur approximately every two weeks. Math 129 is not offered in an on-line or hybrid format.

Q. What is the most common problem that Math 129 students run into?

A. The time commitment. The class time (ten hours every week) is just the tip of the iceberg. Math 129 is really two courses in one semester, so expect to double your usual out-of-class study time and homework time. A common mistake is to treat Math 129 like an ordinary single course. It’s not.

Q. Is on-line homework or testing required?

A. Depending on the instructor, on-line homework could be required. However, the instructor assigned to teach Math 129 during the 2015-2016 school year does not require on-line homework. Homework is assigned from the textbook and collected on exam days. All exams are handwritten exams (no multiple choice tests and no Scantrons) and grading is based on mathematical accuracy, completeness, and the correct use of notation.

Q. What textbook is used for Math 129? Is it required?

A. The current textbook is Elayn Martin-Gay’s Beginning and Intermediate Algebra, 5th edition. The book is required and should be brought to class every day. The course will cover the entire book.

Q. What is the grading policy for Math 129?

A. Most of your grade is determined by the exams. Seven chapter tests are given (with the lowest score dropped), as is a comprehensive final exam (which is never dropped). The chapter tests are 70% of your grade, the final is 15% of your grade, and the homework and quizzes together constitute the remaining 15%.

Q. Is attendance mandatory?

A. Yes. Skipping class is the best way to fall behind and earn a low (or even failing) grade. Reasonable accommodation will be made for emergencies, but students are expected to make their best effort to attend every day. In keeping with Los Rios policy, students will be dropped for excessive absenteeism.

Q. Can students with learning disabilities take Math 129?

A. A good-faith effort is always made to provide reasonable accommodation. However, students who need to work slowly to maintain their accuracy should carefully take into account the challenges of an accelerated course. Time-and-a-half on exams is not difficult to provide, but Math 129 also includes dozens of short in-class quizzes that are immediately followed by demonstrations of their solutions; there is no satisfactory way to provide extra time on such quizzes.

Q. Is extra credit available?

A. Short answer: no. Longer answer: A few (but not many) exams or quizzes will offer optional problems that earn extra points for students who successfully solve them, but Math 129 is not a class where students can compensate for bad exam scores with projects or other alternative assignments.

Q. Is Math 129 offered during summer session?

A. Please tell me you’re kidding!

Thursday, December 17, 2015

Getting a copy of Stroll

A Stroll through Calculus covers many of the concepts of calculus in an informal way with little more than algebra (and later, some trig). It's an attempt to help people understand what's going on without intimidating proofs or formalities, because the basic notions of calculus are both straightforward and elegant. Although Stroll is listed a a textbook for my courses, I put copies on reserve in the library so that I'm not forcing any of my students to buy my book. However, Stroll is listed by the ARC bookstore as a “required” text because that way those of you who want to purchase it can use financial aid resources to do so; otherwise you couldn't.

Here are instructions for obtaining a discounted copy ($31.95, instead of the marked-up bookstore price) directly from Cognella, the publisher:

Step 1: Log on to
Step 2: Create an account or log on if you have an existing account.
Step 3: Follow the step-by-step instructions through the ordering process. [You can buy Stroll as a textbook for my calculus class or my accelerated algebra class; it makes no difference.] Payment can be made with any major credit card.
Step 4: After your purchase, you will have access to a partial pdf of the book by logging on to your account and clicking My Digital Materials. If you bought the complete e-book edition, you will have access to the entire book. [A word of warning from me: The e-book is a time-limited edition, so read the fine print.]

Any problems should be reported via e-mail to or by phone to 800.200.3908 ext. 503.

By the way, after one of my students obtains a copy of Stroll, I will refund my author's royalty to them. I'm not looking to harvest my class for income.

Friday, August 07, 2015

Getting help at ARC

Every student has had the experience of getting stuck. Not every student enjoys the experience of getting unstuck. In many cases, the solution is as simple as finding the right source of assistance.

1 Ask your teacher. Both in class and in office hours, your instructor will be available to answer questions and will expect questions. Although class time is devoted to learning new material and reviewing old material, it's not just a matter of your teacher telling you things. It should be a discussion, where you feel free to ask questions. Contact the instructor by e-mail when you need to.

2 Visit the Learning Resource Center. The college's LRC offers drop-in tutoring at many different times during the week and is usually fully operational by the second week of class. Don't hesitate to drop in, sign up, and take advantage of the LRC's tutors and assistants.

3 If you're a science, engineering, or math student, go to MESA, the Mathematics, Engineering, and Science Achievement program, which is housed in Room 131.

4 Form your own study group. Your instructor will be passing around a sign-up list for people who want to swap contact information to organize study groups.

5 Talk to a counselor about your education plan and get reliable information about the right classes to take.

6 Visit the Student Services building and get direct assistance from Financial Aid or Disabled Student Programs & Services or many other support programs.

Here is a comprehensive link to ARC Support Services, with individual links to many different programs. If you have not browsed this before, it will be worth a visit: Help