Algebra II - Textbook for Students of Mathematics

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Real numbers.

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Quadratic equations; systems of nonlinear equations; resolution of inequalities. Grade 9: Elements of set theory. Powers and roots. Equations and inequalities, and systems thereof.

Algebra II

Elements of trigonometry. Elements of combinatorics and probability theory. Broadly similar questions have been asked elsewhere, however the suggestions made there are not satisfactory for my purposes. The English translations of Gelfand's books are good; however they are not a sufficiently broad introduction to high school algebra, and do not have enough material on computational technique. They are more in the nature of supplements to an ordinary textbook.

Some 19th century books like Hall and Knight have been suggested. On conceptual material, these tend to be too old in language and outlook. Basic Mathematics by Serge Lang seems more to dabble in various topics than to provide a thorough introduction to algebra. I am not inclined towards books with a very strong "New Math" orientation France, for example.

Also, previous questions have perhaps focused implicitly on material in English. I have in mind a student who can also easily read French, German or Hebrew if something better can be found in those languages.

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I'd like to clarify that I'm not asking for something identical to these books, just something as close as possible to their spirit. Fundamentally, this means: 1.

It is a substitute for, rather than just a complement to, a regular school algebra textbook. It is directed at the most able students. It conveys the message that proofs and creative problem-solving are central to mathematics. Here is my second try. I give some references for Olympiad-style problem solving. Hopefully you'll find something useful in each of them. Very student-friendly. The Art and Craft of Problem-Solving teaches basic-level problem solving, including an algebra section.

Problem-solving strategies by Engel is a famous compendium of problems. The focus being on effective problem-solving, theory is really scant but perusing the algebra sections you may find interesting problems. Putnam and Beyond by Gelca and Andreescu is a textbook focusing on undergraduate-level contests. Here you can find many challenging problems from areas usually excluded from high school contests e. Polynomials by Barbeau is a more leisurely treatment of the basic theory of polynomials in case you're dissatisfied with any of the previous suggestions.

Complex Numbers from A to Z by Andreescu and Andrica is a comprehensive exposition about complex numbers.

If you do have to teach this topic, I strongly recommend you to take a look. As a final warning, I must tell you that at least in my own experience contest-geared textbooks tend to focus in quick development of problem-solving skills rather than rigorous mathematical exposition. You may want to consider other kind of textbook to compensate for this. D'Angelo and Douglas B.

It covers a broad array of undergraduate-level topics in a self-contained way and starting from basic notions that are likely to be familiar to the kind of student you describe mathematical logic, methods of proof, sets and functions. The authors present a blend of rigorous theoretical exposition with a practical problem-solving approach through lots of exercises.

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However a disadvantage is that the scope of some topics is rather limited most likely due to constraints of space, but I think this is inevitable given the number of subjects covered. Hope you find it useful! I just saw this today, two years later. There is an organization and website geared specifically to these types of young students. It's called, "Art of Problem Solving. The banner page states, "Is math class too easy for you? That means Westport students focus only on linear functions in Algebra I, taught in seventh, eighth or ninth grade depending on student ability, and leave quadratics and exponents to Algebra II, eliminating the overlap and repetition typical of most textbooks and curriculum guidelines.

Westport has also scaled back exercises like long formal proofs in geometry, revising lessons and homework assignments to teach students to defend their answers to math problems as a matter of routine rather than repeatedly writing them out. In , the National Council of Teachers of Mathematics called for a tighter focus on basic math skills.

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Two years later, a federal panel appointed by President George W. Westport school officials say their less-is-more approach has already resulted in less review in math classes, higher standardized test scores and more students taking advanced math classes. Advanced Placement calculus and statistics classes enrolled students this year, from in , and a record 44 students will be able to take multivariable calculus this fall, up from four in Hank Kepner, president of the National Council of Teachers of Mathematics, said that most schools choose among prepackaged math curriculums, which have to be expansive enough to meet wide-ranging standards for every state, and that he had not heard of another district trying to write its own.

Her company spends two years developing a curriculum using hundreds of math specialists and field-testing in schools. But textbooks are not immune to the streamlining trend: Houghton Mifflin Harcourt has written an Algebra I textbook for Florida schools that is about pages shorter than the 1,page national version.

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Here in Westport, the math curriculum has been compiled from original lessons and assignments as well as material adapted from Web sites, books, training sessions and conferences. Math teachers say their curriculum seeks to balance traditional teacher-directed instruction with student-exploration exercises, and in some cases diverges from Connecticut standards, which, for instance, call for quadratic equations to be taught in Algebra I.

In interviews, several Westport teachers and parents said the slower pace has helped their children focus more deeply on difficult concepts, and students say the shift online has made math easier to understand with cool graphics, animation and real-world context like global warming.