How to Use This Book as a Student

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Hey hey, welcome to Prep for College Math! Here are some basic tips that you should keep in mind as we get started.

When you come across "Examples," it's a good idea to pause and think about them a little bit before reading on, but I am intending to show you something via the solution! Meanwhile, when you see something labeled "Exercise," I am expecting you to give it a shot on your own before opening the "Answer" tab.
Similarly, in the exercise list marked "E" for each section, you should be doing these problems on your own, without looking back at notes or Google or anything, the majority of the time! Whenever a student is like, "I get all the homework problems right, but when I get to the exam, I can't do it," that's code for, "I looked up how to do every homework problem and it was a total waste of my time because that doesn't effectively integrate the skills into my mental toolbox." Treat exercises like mini-exams, and you will be fine when real exams come along. See below for a more detailed step-by-step on homework and learning techniques.
I do intend for you to eventually do every problem in the Exercises section, because sometimes a problem is didactic and there is something for you to ponder and learn from it. Sometimes concepts don't make it into the section, but I still want to expose you to them, so they appear in the exercises. Challenge problems will have more explanation in the "Answer" tab than others, but you should stretch your critical thinking skills before resorting to reading that.
Almost everything in this book is designed to be done without a calculator. When I want you to use calculators, I'll alert you and tell you how, but the basic skills and knowledge covered here is all completely reasonable to expect students to do without technology. You'll notice that none of the numbers turn out devastatingly gross, because I expect you to be using mental math or very quick scratch work. You'll also notice that we learn a lot about what functions tend to look like, because you need to have a sense going forward of how they behave. If your professor tells you, "This population exhibits exponential growth," they expect you to be aware of what an exponential function looks like without pulling out your TI-84. By the end of this class, you should be able to sketch graphs of simple functions using basic knowledge and transformation tricks.
I've provided a study guide at the end of each chapter, but it is much more valuable for you to write your own. Mainly I'm trying to compile a quick reference for you to flip back to later on if you want to recall a detail without clicking through the whole chapter. I highly recommend that you use it as a skeleton to construct your own study guides, in which you should definitely write out example problems! Staring at my lists and bullet points with glassy eyes will do you almost no good compared to doing problems.
I'm writing this book just the way I talk when I'm teaching, which is to say, I'm leaning heavily on what I think is important for you to take away in the end, and I'm goofing off while I'm doing it. There are more "rigorous" ways to say everything in math, and you'll find them in other textbooks, and eventually you will probably have to cope with reading more jargon. I just intend this book to be like a "No Tears" math crash course. Like those "No Tears" kids' shampoo bottles, the ones that look like fish? You remember.

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If you're using this book for MATH040 at Siena College, you will be starting from the beginning and mostly not doing Chapters 7 and 8. If you intend to go straight on into MATH110 (Calculus I) afterwards, you should take some time during the winter or summer break to work through those final chapters on your own, so you're not totally in the dark on those final subjects. I'll put a study schedule in the Appendix for you.
On the other hand, if you're using this book for MATH101 at Siena, you will be skipping significant portions of Chapters 1-3 and going all the way through the rest of the material. If you're rusty on anything basic, you can always look back in detail at the sections we skip. If you want a quick reference on the topics, I recommend just looking at the study guides at the end of each chapter.

How to Succeed in Math

The process of studying math is really unique compared to studying other subjects. The most effective and time-efficient thing you can do is homework/practice problems! Here is how to do homework:

Problems in the Exercises sections come in type "blocks." In each one, start by doing all the odd numbered problems. On whatever type you're struggling with, go back and do the evens for more practice, or use them later when reviewing for exams. Eventually, all problems should be done in some way (as review, used in a practice exam, etc.) as there aren't a TON of them.
After each class session where you cover a section, sit down for a 1-2 hr block of time and go through any examples/exercises from the section that weren't covered in class, and then move to the related Exercises section. For each problem,
1. First attempt to figure out the problem BY YOURSELF. Try for a few minutes. DO NOT look at the answers.
2. If you're totally lost, review the section and look at the examples and exercises for clues (open in a separate tab so you can flip back and forth).
3. Come back to the problem and try again to do it without looking at anything else!
4. When you're finished with a whole block, open the answer and compare. If any of your answers don't match, go back and figure out what you did wrong. This is where the real learning happens!
5. Make a note of any problems you can't figure out completely, and go to office hours to have them specifically explained. That's what office hours are for!!! Every single successful student that I poll after a course says that the big factor in their success was coming to office hours.

Here are other learning strategies to try during the rest of your study time:

When reading the textbook, preview by scanning and making up questions related to the material so you can actively look for the answers.
As you read, paraphrase material back to yourself.
Preview before class (if only for 10 min); go to class and take notes by hand; review after class (if only for 5 min).
Teach the material to a real or imagined audience.
Work in pairs or groups.
Hand-write a study guide or "cheat sheet" even if you're not allowed to use it on the exam. The magic is in making it yourself.
Make up practice exams and simulate testing environment for yourself.

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