Seven Math Books for Seven Math Subjects You can Learn Without Calculus | Summary and Q&A

TL;DR

Learn advanced math subjects without calculus through seven recommended books on graph theory, proof writing, set theory, number theory, linear algebra, abstract algebra, and probability.

Key Insights

• 📈 Graph theory by Ronald Gould is a deep introductory book suitable for beginners in graph theory, providing exercises and examples (subject: graph theory).
• ✍️ A book on proof writing covers multiple math subjects, preparing students for advanced math classes (subject: proof writing).
• 😫 "Naive Set Theory" by Paul Halmos is an easier-to-read classic book on set theory (subject: set theory).
• #️⃣ "Number Theory" by Calvin Long is a highly recommended book for beginners in number theory, offering exercises and solutions (subject: number theory).
• 📔 "Linear Algebra" by Howard Anton is a beginner-friendly book that covers material commonly taught in college linear algebra courses (subject: linear algebra).
• 📔 Abstract algebra, covered in the "Abstract Algebra: A First Course" by Saracino, requires some proof writing experience but is accessible for beginners (subject: abstract algebra).
• 🛟 Sheldon Ross's "A First Course in Probability" serves as an excellent book for learning probability theory, with some sections requiring calculus (subject: probability).

Transcript

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Questions & Answers

Q: How can I learn advanced math subjects without knowledge of calculus?

You can explore graph theory, proof writing, set theory, number theory, linear algebra, abstract algebra, and probability through the recommended books discussed in the video.

Q: Are the recommended books suitable for beginners?

Yes, most of the recommended books are beginner-friendly and provide exercises and examples to help in your learning process.

Q: Do the recommended books include solutions to exercises?

While some books do not provide solutions to all exercises, many of them, especially in linear algebra and number theory, have solutions or hints available.

Q: Can I self-teach myself these math subjects using the recommended books?

Absolutely! These books are perfect for self-study, as they are well-written, contain exercises, and offer solutions for practice.

Summary & Key Takeaways

• Seven math books are recommended for learning advanced subjects without calculus, including graph theory, proof writing, set theory, number theory, linear algebra, abstract algebra, and probability.

• Each book is described, highlighting its content, readability, exercises, and solutions.

• The books cover a range of math subjects and are suitable for beginners and self-study.