Powerful ideas from top nonfiction
Try Blinkist to get the key ideas from 7,500+ bestselling nonfiction titles and podcasts. Listen or read in just 15 minutes.
Get started
Blink 3 of 8 - The 5 AM Club
by Robin Sharma
Elements of Algebra summary
Leonhard Euler
Brief summary
Elements of Algebra by Leonhard Euler is a classic mathematical text that covers a wide range of algebraic topics, from basic operations to the theory of equations. It provides a solid foundation for understanding and applying algebra in various fields.
Topics
Table of Contents
Elements of Algebra
Summary of key ideas
The Essence of Algebra
In Elements of Algebra, Leonhard Euler provides a comprehensive and accessible introduction to the fundamental concepts of algebra. He begins by laying out the basic principles of arithmetic, including the properties of numbers and operations such as addition, subtraction, multiplication, and division. Euler then moves on to explore the concept of a variable and its role in algebraic expressions, equations, and inequalities.
One of the key themes Euler explores is the idea of a function. He explains how a function represents a relationship between two sets of numbers, and introduces concepts such as domain, range, and the graph of a function. Euler also discusses various types of functions, including linear, quadratic, exponential, and logarithmic functions.
Equations and Inequalities
Next, Euler delves into the study of equations and inequalities. He explains how to solve linear and quadratic equations, as well as higher-degree polynomial equations. Euler introduces techniques such as factoring, completing the square, and using the quadratic formula to find solutions to these equations. He also discusses the nature of solutions, including real and complex roots.
In the section on inequalities, Euler explores how to solve and graph inequalities, and how to use inequalities to represent real-world situations. He also discusses systems of equations and inequalities, showing how they can be solved using a variety of methods, including substitution, elimination, and graphing.
Polynomials and Rational Expressions
Euler then turns his attention to polynomials and rational expressions. He explains the basic properties of polynomials, including their degree, leading coefficient, and roots. He also introduces techniques for factoring polynomials, including the factor theorem and synthetic division.
When it comes to rational expressions, Euler discusses their simplification, multiplication, division, addition, and subtraction. He also explores the concept of rational equations, showing how to solve them by finding a common denominator and applying the principles of solving linear equations.
Exponents, Radicals, and Complex Numbers
Another important topic Euler covers is exponents and radicals. He explains the properties of exponents, including rules for multiplication, division, and raising a power to a power. He also introduces the concept of a radical and explores how to simplify and manipulate radical expressions.
In the later part of the book, Euler introduces complex numbers, which are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit (√-1). He explains the basic operations on complex numbers, including addition, subtraction, multiplication, division, and the complex conjugate.
Applications and Conclusion
In the final sections of Elements of Algebra, Euler provides a variety of applications of algebra to real-world problems. He demonstrates how algebraic principles can be used to solve problems in geometry, physics, and engineering. He also discusses the historical development of algebra and its significance in the advancement of mathematics.
In conclusion, Euler's Elements of Algebra provides a thorough foundation in algebraic concepts and techniques, making it an invaluable resource for students and enthusiasts of mathematics. With its clear explanations and numerous examples, the book serves as an excellent starting point for further exploration of algebra and its applications.
How do we create content on this page?
More knowledge in less time
Read or listen
Get the key ideas from nonfiction bestsellers in minutes, not hours.
Find your next read
Get book lists curated by experts and personalized recommendations.
Shortcasts New
We’ve teamed up with podcast creators to bring you key insights from podcasts.
What is Elements of Algebra about?
Elements of Algebra by Leonhard Euler is a classic mathematical text that delves into the fundamental principles of algebra. Originally published in the 18th century, Euler presents a comprehensive and systematic exploration of algebraic concepts, equations, and operations. This influential work continues to be a valuable resource for students and mathematicians alike.
Elements of Algebra Review
Elements of Algebra by Leonhard Euler (1770) is a fundamental work exploring algebra's core concepts. Here's why this book is worth your attention:
- Explains complex mathematical concepts clearly, making it accessible for all levels of readers.
- Demonstrates the beauty and elegance of algebra through practical examples.
- Keeps readers engaged with its insightful problem-solving techniques that stimulate critical thinking.
Who should read Elements of Algebra?
Students and educators studying or teaching algebra
Math enthusiasts looking to deepen their understanding of algebraic concepts
Individuals seeking a comprehensive and clear explanation of algebraic principles
Categories with Elements of Algebra
Book summaries like Elements of Algebra
People ❤️ Blinkist
Sven O.
It's highly addictive to get core insights on personally relevant topics without repetition or triviality. Added to that the apps ability to suggest kindred interests opens up a foundation of knowledge.
Thi Viet Quynh N.
Great app. Good selection of book summaries you can read or listen to while commuting. Instead of scrolling through your social media news feed, this is a much better way to spend your spare time in my opinion.
Jonathan A.
Life changing. The concept of being able to grasp a book's main point in such a short time truly opens multiple opportunities to grow every area of your life at a faster rate.
Renee D.
Great app. Addicting. Perfect for wait times, morning coffee, evening before bed. Extremely well written, thorough, easy to use.
People also liked these summaries
4.7 Stars
Average ratings on iOS and Google Play
38 Million
Downloads on all platforms
10+ years
Experience igniting personal growth
Elements of Algebra FAQs
What is the main message of Elements of Algebra?
The main message of Elements of Algebra is to provide a comprehensive understanding of algebraic concepts.
How long does it take to read Elements of Algebra?
Reading Elements of Algebra takes some time, but the Blinkist summary can be read in a fraction of that.
Is Elements of Algebra a good book? Is it worth reading?
Elements of Algebra is a valuable read for those interested in deepening their algebraic knowledge.
Who is the author of Elements of Algebra?
The author of Elements of Algebra is Leonhard Euler.
What to read after Elements of Algebra?
If you're wondering what to read next after Elements of Algebra, here are some recommendations we suggest:
- Where Good Ideas Come From by Steven Johnson
- Incognito by David Eagleman
- God Is Not Great by Christopher Hitchens
- A Brief History of Time by Stephen Hawking
- The Selfish Gene by Richard Dawkins
- Simply Complexity by Neil F. Johnson
- Antifragile by Nassim Nicholas Taleb
- Physics of the Future by Michio Kaku
- The Black Swan by Nassim Nicholas Taleb
- Musicophilia by Oliver Sacks