Math 111 Textbook Pdf Download !!EXCLUSIVE!!
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Reading a mathematics text is very different from reading ordinary English. Trying to read math the same way as a novel or a history text is certain to cause you trouble. Math text typically alternates passages of explanation in English with pieces of mathematics. Even its English, however, is of a special and stylized kind.
With actual mathematics (equations and such), the trick is simply to see how each line follows from the line before. If the step is especially obscure, the author may provide some written explanation. But be sure that you understand where each line comes from, before you go on to the next line. If you skip even one step, the rest of the steps will make little or no sense to you.
It is best to read mathematics with pencil and paper at hand, and to reproduce it yourself as you go along. But do not merely write down what you see in the book. Instead, try to work out each line for yourself, step by step, with the author.
Really important mathematical passages are problems that the author has worked out in detail. Successful students rely on these very heavily. One widely used series of review texts in mathematics consists entirely of solved problems.
I am writing an ODEs textbook for second year students and I would like to get inspirations on general good designs on undergraduate textbooks taught in the first two years (i.e. calculus, linear algebra, real analysis and ODEs ) that enhance student understanding .
I was debating whether to put this post here or in the math-educators stackexchange, but I am curious to hear of design strategies seen in research/graduate textbooks that haven't trickled down to undergraduate textbooks. But if it doesn't fit here, tell me and I will promptly remove it.
a key difference with undergraduate students as opposed to graduate students, is that one should spent more time motivating the material. One idea is introducing methods and theorems through examples and especially applied ones (eg. from physics and economics). The design principle here is going from the concrete to the abstract. Di Prima's ODEs textbook achieves this beautifully.
I personally enjoyed graduate textbooks that also provided me with short code programs and guided exploratory exercises. Like "Computational Methods for Fluid Dynamics" by Peric etal. It is also done in many ODE textbook such as Boyce's. This is doable with ODEs if you are working with MATLAB, which provides ODE solver packages.
In terms of designing exercises, I liked it when the first few questions were broken down into multiple baby questions, which also taught me how to ask questions so as to make a large question more manageable. I saw this in Pugh's real analysis textbook.
I've published a number of undergraduate and graduate science books, some heavy in mathematics, but no true mathematics textbooks. I've thought long and hard about how to design and craft them, and have several professional calligraphers, type designers, book designers in my immediate family, and they (and of course my students) have given lots of great feedback.
My personal writing style (and indeed academic/professional style) is to be as visual as possible. (Try to get your publisher to agree to full-color graphics.) Many students will remember topics better with careful graphics, find topics by flipping through the book faster, and so on. Two of my favorite math book presentations are Visual group theory by Nathan Carter and An illustrated theory of numbers by Martin Weissman, both of which should give you ideas. This latter uses a great $\LaTeX$ style sheet, which I am sure is freely available. Also, be sure to read the master--Ed Tufte--and his great books, such as Envisioning information.
Ostensibly, the question is about "design principles," but the follow-up examples are largely about writing/pedagogy decisions. So this seems to be a question about how to write a textbook that's good for student learning (broadly speaking) rather than the visual/physical design.
Look at other textbooks in the subject closely. What are you trying to offer that those books don't already offer? If you go to a publisher, they will make you go through this process, for good reasons.
I'm one of many volunteers recording textbooks for use by reading-impaired students. We often encounter books whose pages remind me of refrigerator doors they're so cluttered with text in various colored boxes and presented with great typographical variety. These books have been "designed" by someone according to some logic, I guess, but each book requires someone in our organization to devise rules for the several narrators to follow in sequencing and naming the stuff as "box'" "margin note," etc. It seems to me that if authors have some valuable information, they should be able to set it out in a logical sequence that requires no gussying up. I suspect that the need for this sort of "design" is merely an attempt to disguise the authors' failure to organize their material. Publishers should reject any manuscript showing such lack of organization.
The way you read a math textbook is different from the traditional way students are taught to read textbooks in high school or college. Students are taught to read quickly or skim the material. If you do not understand a word, you are supposed to keep on reading. Instructors of other courses want students to continue to read so they can pick up the unknown words and their meanings from context.
This reading technique may work with your other classes, but using it in your math course will be totally confusing. By skipping some major concept words or bold-print words, you will not understand the math textbook or be able to do the homework. Reading a math textbook takes more time and concentration than reading your other textbooks.
If you have a reading problem, it would be wise to take a developmental reading course before taking math. This is especially true with math reform delivery, where reading and writing are more emphasized. Reform math classes deal more with word problems than do traditional math courses. If you cannot take the developmental reading course before taking math, then take it during the same semester as the math course.
Step 1 - Skim the assigned reading material. Skim the material to get the general idea about the major topics. Read the chapter introduction and each section summary. You do not want to learn the material at this time; you simply want to get an overview of the assignment. Then think about similar math topics that you already know.
Step 3 - Put all your concentration into reading. While reading the textbook, highlight the material that is important to you. However, do not over-highlight because the material will not being narrowed down enough for future study. Especially highlight the material that is also discussed in the lecture. Material discussed both in the textbook and lecture usually appears on the test. The purpose for highlighting is to emphasize the important material for future study. Do not skip reading assignments.
Step 4 - When you get to the examples, go through each step. If the example skips any steps, make sure you write down each one of those skipped steps in the textbook for better understanding. Later on, when you go back and review, the steps are already filled in. You will understand how each step was completed. Also, by filling in the extra steps, you are starting to over-learn the material for better recall on future tests.
Step 8 - Reflect on what you have read. Combine what you already know with the new information that you just read. Think about how this new information enhances your math knowledge. Prepare questions for your instructor on the confusing information. Ask those questions at the next class meeting.
By using this reading technique, you have narrowed down the important material to be learned. You have skimmed the textbook to get an overview of the assignment. You have
carefully read the material and highlighted the important parts. You then added to your notetaking glossary unknown words or concepts.
The structure of a math textbook should follow a logical progression from basic concepts to more complex ones. It should also include clear explanations, examples, and practice problems to reinforce the material. Additionally, it is important to include visuals such as diagrams and graphs to aid in understanding.
A math textbook should cover all the necessary concepts and skills for the intended audience. This includes definitions, formulas, theorems, and problem-solving techniques. It is also helpful to include real-world applications to make the material more relatable.
Diagrams are a useful tool for visualizing mathematical concepts. They should be used to supplement written explanations and should be clear and easy to understand. It is important to label all parts of the diagram and provide a brief explanation of its purpose.
Incorporating a program to draw diagrams can be beneficial for both the author and the reader. For the author, it can save time and improve the accuracy of the diagrams. For the reader, it can enhance the learning experience and make the material more interactive. However, it is important to ensure that the program is user-friendly and does not distract from the main content of the textbook.
To make your math textbook engaging, it is important to present the material in a clear and concise manner. Additionally, including real-world examples and interactive elements such as practice problems and activities can help keep readers interested. Using a variety of visuals, such as diagrams and graphs, can also make the material more visually appealing.
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