Mathematics: Fun tricks for everybody
Mathematics from high school to university
What you will learn
Creative problem solving, with fun tricks and geometrical illustrations of the results.
How to derive the formula for the sum of squares of all natural numbers from 1 to n.
How to derive the formulas for partial sums for two very important examples of arithmetic progressions: 1+2+...+n and 1+3+5+...+(2n-1).
How to derive the general formula for partial sums of geometric progressions; an important example of the sum of all the natural powers (from 1 to n) of 1/2.
How to derive some less known formulas, using cool computational tricks.
How to prove divisibility in some simple cases, using very basic (but fun) reasoning.
You will learn (from an article) how to convert infinite periodic decimal expansions into fractions, by smart substitutions and solving linear equations.
You will learn (from an article) some basics about continued fractions (CF), and how to recognise irrational surds from their infinite periodic CF-expansions.
You will learn (from an article) about an interesting family of nested square roots and how to prove that some members of this family are... integers!
Why take this course?
Unlock the Beauty of Mathematics: "Mathematics: Fun Tricks for Everyone" with Hania Uscka-Wehlou
🚀 Course Title: Mathematics: Fun Tricks for Everybody 🎓 Instructor: Hania Uscka-Wehlou 🧮 Course Headline: From High School to University - Discover the Aesthetic Side of Math!
Course Description: Math is not just a set of tools; it's an art form that captivates the mind and satisfies our innate quest for understanding. In this course, we explore the aesthetic aspect of mathematics that transcends its practical applications in engineering and finance. 🎨💭
Join us as we delve into the world of numbers with a fresh perspective, where you'll fall in love (or rekindle your affection) with the subject that powers logic and reasoning. Whether you're a math enthusiast or simply curious, this course promises to illuminate the beauty within the discipline.
- 🔍 Mathematics as Art: Learn to appreciate mathematics beyond its utilitarian uses, and discover how it can provide intellectual joy and fulfillment.
- 🚀 Simple Tricks for Complex Problems: Master the art of solving problems with deceptively simple techniques, without delving into intricate theories.
- 📚 Comprehensive Learning Experience: Engage with a blend of video content and written articles to explore a variety of mathematical concepts.
What You'll Learn:
Section 1: Sums & Products in Sequences 🔢
- Discover the secrets behind calculating sums in arithmetic and geometric progressions, as well as the sequence of squares.
- Uncover two lesser-known sequences and their fascinating properties.
- Learn a formula for finding the product in a unique sequence, complete with geometrical insights! 📊
Section 2: Divisibility & Inequality 🔄
- Explore two essential divisibility problems that will help you quickly determine if numbers are divisible.
- Understand a surprising inequality and its implications in mathematics.
Section 3: Eliminating Operations with Substitutions 🧩
- Dive into the world of infinite periodic decimal expansions, continued-fraction expansions, and nested square roots.
- Discover how smart substitutions can simplify complex mathematical problems to their essence. 🎬
Extras:
- Get an overview of all the courses we offer to enhance your learning experience.
- Catch a glimpse into our exciting future course plans, with tentative release dates! 🚀✨
Engage with Mathematics in a New Light: Mathematics: Fun Tricks for Everybody is not just another math course; it's an invitation to rediscover the elegance and charm of mathematics. Whether you're a high school student or a university scholar, this course is designed to spark your curiosity and provide you with tools to approach problems in innovative ways. 🌟
Enroll now and be part of a community that values the beauty and fun of mathematical exploration! 🎉
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Our review
***** Course Review for Mathematical Problem Solving *****
Overall Rating: 4.75/5
Pros:
- Engaging Content: The course is described as fun and engaging, with interesting tricks and exercises presented in short lectures that facilitate learning and training in problem-solving techniques.
- Teaching Methodology: The instructor's teaching method is highlighted as exceptional, focusing on guiding students to the discovery of mathematical concepts rather than simply presenting the steps to a solution. This approach fosters a deeper understanding and appreciation for the subject matter.
- High Quality of Instruction: Reviews mention that the course content is clearly explained, with the instructor being characterized as a golden teacher who can inspire students to learn mathematics effectively.
- Appeal to Different Learning Styles: The course is noted to be very helpful and suitable for high-school students, as well as for individuals interested in mathematics. It also seems to cater to different learning speeds, with some learners finding the pace ideal for slow and precise explanations.
- Diverse Problem Set: The selection of problems provided in the course is commended for being well-illustrated and interesting, offering new insights to seasoned learners and enthusiasts alike.
- Global Appeal: The course has garnered positive feedback from diverse regions, including India, indicating its potential for international audiences.
Cons:
- Lack of Derivation Guidance: Some reviewers expressed a desire for additional guidance on how to approach the derivation steps in certain problems. They mentioned that while the mathematics is known, understanding the ideas behind deriving solutions is an area where further clarification would be beneficial.
- Systematic Approach: There is a mention of a need for a more systematic approach to developing problem-solving strategies, which could complement the intuitive and demonstrative teaching methods already in place.
Additional Feedback:
- Interactive Learning Experience: One user noted the value of pausing and reflecting on the lectures, suggesting that this interactive element is a significant aspect of the learning experience.
- Long-term Impact: Another reviewer pointed out that insights from the course can surface long after the lessons have been studied, highlighting the course's impact over time.
Recommendations for Improvement:
- Supplementary Resources: It may be beneficial to provide supplementary materials or guidance on developing problem-solving strategies and approaches, especially for those who are still mastering the initial steps of mathematical thinking.
- Training for Educators: The positive feedback suggests that the instructor's method could be valuable for training students and educators alike, potentially leading to expanded course offerings or workshops in various educational institutions.
Final Thoughts: This course is highly recommended for anyone interested in mathematics, from high-school students to lifelong learners. Its effectiveness lies in its ability to not only teach mathematical principles but also to inspire a love for the subject and an appreciation for the art of mathematical discovery. The course's global positive reception indicates its universal appeal and the instructor's exceptional teaching abilities. To further enhance the learning experience, additional resources or explanations on developing problem-solving approaches could be integrated into future iterations of the course.