Matemática do COMEÇO ao FIM! Todos os livros que você precisará.

Summary

In this video, the speaker presents a comprehensive guide to essential mathematics books for students from high school through to graduate studies. Covering foundational topics like set theory and functions, calculus, linear algebra, and differential equations, the speaker recommends specific texts suited for various mathematical disciplines. They emphasize the importance of a solid base in mathematics for courses in physics, engineering, and education. The video serves as a valuable resource for anyone pursuing mathematics, providing insights into key literature that supports both theoretical understanding and practical application.

Takeaways

• 📚 The video recommends a comprehensive list of math books suitable for studying mathematics from the basics to advanced levels, particularly for undergraduate courses.
• 🔍 'Fundamentos da Matemática Elementar' is highlighted as essential for building a strong mathematical foundation, comprising 11 volumes covering basic education content.
• ⌛ If you're short on time, 'Manual Compacto de Matemática' is suggested as a simpler alternative to the foundational collection, covering essential high school topics.
• 📖 For calculus courses, 'Cálculo Volume 1' by Guidorizzi is recommended, especially for those studying mathematics without a strong command of English.
• 📐 A well-structured book on logic, 'Um Convite à Matemática' by Daniel Cordeiro de Moraes Filho, is suggested for learning definitions, theorems, and proof techniques.
• 🌀 In geometry, 'Geometria Euclidiana Plana' by João Lucas offers a condensed version of Euclid's works, tailored for modern mathematical reasoning.
• 🔢 'Curso de Álgebra Linear' by Elon is recommended for linear algebra, with an accompanying exercises book by Ralf Costa Teixeira for practice.
• 📏 For second-semester courses, 'Cálculo Volume 2' and a good linear algebra book are essential for progressing in mathematics.
• 📊 For probability courses, 'Probabilidade: Um Curso Moderno com Aplicações' by Sheldon Ross is recommended for its thorough treatment of the subject.
• 📖 'Equações Diferenciais Elementares' by Boice and DiPrima is suggested for differential equations, covering both ordinary and partial equations comprehensively.

Q & A

What is the purpose of the video?

The video aims to provide a comprehensive list of books for studying mathematics from basic to advanced levels, suitable for undergraduate courses.

What does the presenter mean by 'from the beginning to the end of mathematics'?

This phrase refers to covering the entire scope of topics typically found in a mathematics undergraduate curriculum, including some advanced subjects.

Which book is recommended for foundational mathematics?

The 'Fundamentos da Matemática Elementar' series is recommended for building a solid foundation in mathematics.

What book does the presenter suggest for those short on time?

For those pressed for time, the 'Manual Compacto de Matemática do Ensino Médio' is suggested as a simpler and more direct alternative.

What is the best calculus book for students who struggle with English?

The presenter recommends 'Cálculo Volume 1' by Guidorizzi as the best choice for students who might have difficulty with English texts.

What course does the book 'Um Convite à Matemática' correspond to?

This book is recommended for the introductory logic course in a mathematics curriculum.

What is the significance of learning Euclidean geometry?

Understanding Euclidean geometry is crucial as it forms the basis for advanced studies using logical reasoning and proofs.

Which book is recommended for linear algebra?

The book by Elon is highly recommended for linear algebra, along with an accompanying exercises book by Ralf Costa Teixeira.

What topic does the book by José Santos cover?

The book by José Santos focuses on number theory, although the presenter expresses a personal disinterest in the subject.

What should students do if they need to study differential equations?

For differential equations, the presenter recommends 'Equações Diferenciais Elementares e Problemas de Valores de Contorno' by Boice and DiPrima.