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OceanSpring
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Can someone tell me if Axler's texts use proofs? I'm looking for a book that teaches proofs at the high school level. Something other than a geometry text.
This course does not focus much on proofs
I don't think there are 'high school level proof'. When I was in HS I trimmed through the Book of Proof. Then, I picked up a set theory book and worked through the various proofs (someone from PF suggested it) and it really was great. I can't say my proofwriting is perfect, but I know the basics well enough to work through Axler's LA and Abbott's Analysis in my first year of undergrad. Velleman also wrote a book on proofs but in my opinion, Book of Proof is straight up better.OceanSpring said:I'm looking for a book that teaches proofs at the high school level. Something other than a geometry text.
The main difference between Algebra and Trig/Precalculus for proofs is the level of mathematical concepts covered. Algebra focuses on basic operations, equations, and functions, while Trig/Precalculus covers more advanced topics such as trigonometry, complex numbers, and vectors. However, both courses use proofs as a way to logically justify mathematical statements.
Axler's textbook uses a more conceptual and intuitive approach to proofs, rather than a purely mechanical one. It emphasizes understanding and reasoning over memorization of formulas and algorithms. The book also includes numerous examples and exercises to help students develop their proof-writing skills.
Yes, this textbook can be used for self-study as it is written in a clear and accessible manner. However, it is recommended to have a basic understanding of Algebra and Trig/Precalculus before diving into the proofs covered in this book.
Axler's textbook provides a strong foundation in proof-writing skills, which is essential for success in higher-level math courses. It also introduces students to advanced topics such as complex numbers and vectors, which are commonly used in higher-level courses. Additionally, the conceptual approach used in this textbook can help students develop a deeper understanding of mathematical concepts.
Yes, there are various online resources available such as practice problems, video lectures, and interactive quizzes that can be used to supplement this textbook. Students can also find solutions to the exercises in the textbook online, which can be helpful for self-study and review.