I offer these notes to anyone who is using this textbook, in the hope that they will be helpful. I am delighted that others are finding these notes helpful - so if you find them helpful, let me know! Here's what one happy reader said: "I have been using your notes (for circular permutations [lesson 55] they were a big help). We live in a remote area of Florida and I don't know any others in this area that are working on Advanced Math." [MFurey]. One of the main reasons I teach the class is because I believe it is important for people to learn the basics of math... I cannot teach everyone, but this is a small way I can help.
Sadly, if you're not in my class (or at least SGC), please don't send me math questions - I'd like to help, but I simply can't answer math questions sent from everyone in the world (sorry!). The co-op is a service provided by SGC to church members; Sovereign Grace Church (SGC) Home Ed Blog (HEA) and HEA Blog co-op documents have the latest info.
A word about data formats: I normally edit my class notes in OpenDocument format (ODF), which is the international open standard for office documents (ISO/IEC 26300:2006). Files ending in ".odt" are OpenDocument text (e.g., word processing format). There are many programs that can read and write this format; two good free ones are LibreOffice and OpenOffice.org, both of which are available for MS Windows, Apple Macintosh, Linuxes, *BSDs, and Unix. (I'm told that Microsoft Office can also read them, but I have not checked.) If you just want to read the notes, you can read the PDF version (PDF is also internationally standardized); there are lots of PDF readers, many free. As a general rule I strongly encourage the use of open data standards (formats that aren't controlled by any one vendor), such as ODF, PDF, and HTML. I also use the international standard format for dates (ISO 8601), YYYY-MM-DD, which helps to avoid confusion in international communication - and it sorts well too.
Syllabus [PDF] | Syllabus [ODF] (It hasn't changed)
Calendar 2013-2014 [PDF] | Calendar 2013-2014 [ODT]
Suggested Schedule [PDF]
Mathematics: What & Why [PDF] | Mathematics: What & Why [ODF] (What Math? is a nice additional essay.)
Show your work (William Mulholland): [PDF] | [ODF]
Notes on Lessons (latest versions):
I typically have notes on the lessons ready the night before, and make minor revisions within the day after class (based on comments during class).
As you do your lesson problems, do one problem and then check the answer (don't do all the problems at once). Otherwise you might practice doing it wrong. Also, if you make a mistake, work hard to figure out exactly why, and then figure out what to change so that you never make that mistake again.
Turn in tests on Sunday in the "HEA Tests" mailbox (lower rightmost box); mailboxes are in the foyer behind the information desk. Parents: Please do a preliminary grading; put a big "check" or "elongated C" (correct) mark by the correct ones, and a big "X" by the incorrect ones. That way, I can concentrate on figuring out partial credit, and you can have immediate information on how well they're doing. Here are some test-taking tips:
After this class, you may be able to answer some of the challenges on this page.
Related - here's a quick cheatsheet on Negative numbers (PDF) | Negative numbers (ODT). If you need this, you shouldn't be in the Advanced Math class - I created this for a junior high school student.
Algebra II is the leading predictor of college and work success.
Modern mathematics has been able to prove many amazing relationships, but like everyone mathematicians can make mistakes. There are efforts to formalize mathematics so that computers can automatically check math proofs to ensure they are correct. You don't need to know about these in detail, but I think you might find them interesting. One of the more intriguing projects to me is metamath. Metamath starts with the extreme basics: set theory (using the usual Zermelo-Fraenkel definitions), propositional calculus (which lets you prove statements about true/false statements), and predicate calculus (which lets you prove statements about objects). From there, they have formally proven that numbers exist and lots of properties about them. You can learn a lot about math just by looking at their proofs, in part because if there is some part you do not understand, you can click on that part to learn more (and repeat as necessary). For example, here is a proof that the product of two negative numbers is positive. They use common math notation:
Legal stuff: The Saxon book is copyrighted, so I cannot post extensive portions of the book. To avoid running afoul of copyright law, I create my own explanations and examples - which means these notes are my own copyrighted work, and are not a derivative of Saxon's work. Having things explained in a different way, with different examples, is better for teaching anyway (because it gives my students more examples to learn from). I do use the same order of instruction as Saxon's book - I don't see how I could avoid doing so while using Saxon as the textbook! I believe this is de minimus (so small as to not matter), but even if it isn't, this use of Saxon's outline is clearly fair use. After all, it is for the purpose of teaching, it's for nonprofit educational purposes, it's clearly transformative (I create new examples and explain things differently instead of just posting the outline), it emphasizes mathematical facts (which cannot be copyrighted), its content is quite different from Saxon's (it merely follows the same order), and it does not diminish Saxon's potential market (if anything, it increases it). Fair use is a critically important part of U.S. law.
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