The Dunning-Kruger Effect and Learning

People tend to be biased when assessing their own abilities; this bias is called the Dunning-Kruger effect. Studies show that the poorer the ability, the greater the difference between one’s overestimate of one’s ability and one’s actual ability. One manifestation of this phenomenon is that people who know nothing about a subject and then learn … Read more

Linear Algebra is Scary, Even for Future Mathematicians

The Calculus of Friendship: What a Teacher and a Student Learned about Live While Corresponding about Math (2009) is a delightful book by Steven Strogatz. Strogatz is Jacob Gould Schurman Professor of Applied Mathematics at Cornell University, and he writes beautifully. The book is about his decades-long correspondence with one of his high-school mathematics teachers, … Read more

What is Infinity?

One of the common errors made by calculus learners is to consider infinity as a number. True, there are number systems such as the extended real number system in which infinity is successfully treated as a number, and you can ponder on them if you wish, but for our purposes at this level of learning … Read more

What is Calculus?

What is calculus and what is it used for? Calculus includes an enormous number of ideas, methods, and applications, and this post is an attempt to provide an overview. Most of the interesting phenomena that are analyzed scientifically involve change. The flow of wind and water, the orbits of the planets, the path of a … Read more

What is Linear Algebra?

Solving systems of equations Solving a single linear equation with one unknown quantity is a task that is studied in elementary school. One proceeds in high school to study more complex equations involving more involved functions. Many problems in mathematics and its scientific applications amount to solving equations, and especially to solving systems of equations. … Read more

How to Concentrate

Concentration is a key skill for becoming a good learner. This is especially true in studying mathematics and physics, where you are continually engaging with new concepts. You also frequently have to mobilize all of your thinking power to grapple with complex problem-solving tasks. This often takes time, so you need to sustain your focused … Read more