Enroll Course: https://www.coursera.org/learn/introduction-to-math
Are you looking to deepen your understanding of mathematics beyond the high school curriculum? Do you want to see how mathematicians approach familiar concepts with fresh perspectives? Then Coursera’s “Invitation to Mathematics” (also known as “הזמנה למתמטיקה”) might be the perfect course for you.
This course is designed to bridge the gap between high school mathematics and university-level studies. It aims to reveal the elegance and interconnectedness of mathematical ideas, preparing students for the rigor and abstract thinking required in higher education. The course is taught from an advanced perspective, encouraging a deeper appreciation for the subject.
The syllabus covers a wide range of essential topics, starting with a thorough exploration of the Pythagorean theorem. It doesn’t just present the theorem; it delves into multiple geometric proofs and its algebraic representation, showcasing how even basic concepts can be understood in novel ways. From there, the course moves on to Pythagorean triples and different ways to represent functions, offering a solid foundation in analytical thinking.
Further units explore the formal definition of a function, understanding function graphs, and extending this to functions of two variables. Trigonometric functions are explained through their geometric meaning, with a focus on sine, cosine, and tangent, including their inverse functions. A significant portion of the course is dedicated to complex numbers, introducing their basic properties, solving equations, and exploring their various representations and applications, including the fascinating roots of unity.
The course then transitions into calculus, introducing the concept of the derivative, its geometric interpretation, and real-world applications. Integral calculus is presented, highlighting its connection to geometric areas. The relationship between integrals and derivatives is explored, leading to the calculation of integrals for elementary functions.
Finally, the course touches upon exponential and logarithmic functions, their interrelationships, and their connection to calculus. It also covers sequences, including arithmetic and geometric progressions, and delves into recursive sequences like the Fibonacci sequence. Mathematical induction is introduced as a powerful proof technique for sequence properties. The course concludes with a real-world problem, demonstrating how the insights gained throughout the curriculum can be applied to solve practical challenges.
“Invitation to Mathematics” is an excellent resource for anyone seeking a more profound and nuanced understanding of mathematics. It’s particularly recommended for students planning to pursue STEM fields at the university level. The course successfully demystifies advanced mathematical concepts, making them accessible and engaging.
Enroll Course: https://www.coursera.org/learn/introduction-to-math