Mathematics Study Tips - Pre- (and post??) pare for lectures

Hey again all. Some time ago, I started writing down what I consider are good tips and practices for studying and getting through mathematics courses at the university level. Click on the "Study Tips" tag to see those. here is another I find myself often saying to struggling students:

To make most of the lectures (the backbone of the course, no?), why not prepare for them. To really make them an integral part of your course experience, why not post-pare for them also!? What do I mean...?

It is commonly accepted that it is easier to remember something when you hear it more than once. Maybe then it is placed in more than one position in your brain, with different associations triggering its location. Maybe it still sits in one location but is better interconnected with other triggers. Maybe I have no idea.

But it would certainly help greatly to not only know what is coming up in the next lecture (check the syllabus online before the meeting), but also to have spent some time in the book on the material before the show. No ?

Preparing for the Lecture

If you know the next lecture is on ( a hypothetical) Section 4.6, say, why not spend 10-15 minutes before the lecture reading through that section? You don't have to understand completely what you are reading. Some of it will make sense, some not. But at least you will be exposed to terms, concepts, boxed items, examples, BEFORE you enter the class to actually see the lecture develop the ideas. This way, the stuff you did understand on first reading will be cemented by the lecture development. You can even relax a bit on this part of the lecture.

When you get to the part of the lecture that comes from material in the book that mystified you, you can then spend some precious attention time focused. Pretty efficient, huh? We, as instructors, really do like to follow the book in many of our courses. Books are written in an organized fashion. We may embellish the material, but the core usually comes from the book.

Your notes in a lecture are an important facet of your eventual understanding. See here for some tips on taking notes.

Post-paring for the lecture

After the lecture is where the fun really starts! Here is my idea for good practice....

Grab a small block of time (another 15 minutes), in a quiet place and free from distractions, somewhere between an hour and three hours after the lecture. It won't take long. Go over your notes slowly and carefully an in your mind, relive the lecture, re-listening to the instructor and imagining the lecture hour unfold. As you f0llow your notes, you will remember things that were said that you did not write down (or finish writing down). Write them down now. You will see examples half-finished. Finish them now. You will references to the book. check them and make a mental note of them, You will make connections that you did not make before. Note them in your notes. You will see thing in your notes that STILL mystify you. Mark them (in red?) with a big question mark. Make a note to yourself to go to your TA or the instructor and ask specifically about these question marks (much of this part is also talked about in my installment of this series on Notes. Take a look there also).

All of this is called "completing the experience". It is a way to make your notes of the lectures a complete and central account of the course, as they should be. And it is a form of studying that WILL pay big dividends as the course progresses.

Try this for a few weeks. It really is a minimal effort for the benefit it offers. You will see improvement.

In bocca al lupo!

Course Pre-req changes....

Here is a heads-up on some course pre-requisite changes that we will be implementing immediately. We will be forcing anyone considering 110.211 Honors Multivariable Calculus to either take 110.201 Linear Algebra or 110.212 Honors Linear Algebra as a co-requisite (at the same time), or to have one of them (or equivalent) as a pre-requisite. If either of our versions of Linear Algebra are to be used as a pre-requisite, then the final grade must be a B+ or better.

The reasons are simple: A good, solid working knowledge of linear algebra is absolutely necessary to fully understand the theoretical underpinning of multivariable calculus. One can say that multivariable calculus IS the non-linear generalization of linear algebra (or that linear algebra is simply the linearization of multivariable calculus). This allows us to concentrate on the calculus nature of the topic without having to focus on leveling the background deficiencies of some of our students. It also will dampen the urge of some of our students to jump into a course they only later realize they are not qualified for. Our version of honors Calculus III is deeply theoretical by design. And we want to focus this level of training on those who definitely will be seeking a major in mathematics, or have a real interest in and dedication to the formal development of the mathematical topic.

As for the co-requisite option, it turns out that how linear algebra is used and developed within vector calculus lends itself well to a side-by-side learning experience.

We will continue to monitor this course (along with its text choice). But for the short term, you must have linear algebra in your back pocket (or promise to attain it) prior to jumping into the deep end of the multivariable calculus pool.

Happy swimming.

Summer Internship Oppo!

Hey, just got word from the Mathematics Research Group over at the National Security Agency (NSA: You know those guys, right?). The Director's Summer Program is a research-based 12 weeks in the summer where one works on issues involving pure mathematics, cryptology and communications technology. It is a paid position, prestigious, and of course highly competitive. It would also be a great career booster, even if you really have no intention of working at the NSA in the future.

The application process is all online, and the deadline is October 15. Give it a look.