Infinity is Really Big

January 15, 2019January 28, 2019

New Video: Macaulay Duration is a Decreasing Function of the Coupon Rate r

Early today I posted my 166th video on problem solving for actuarial exam 2/FM (financial mathematics) on YouTube.

Wow! One-hundred and sixty-six videos on financial mathematics for actuaries?!?! Yes! This has been an almost two-year YouTube project so far. Here’s the video that I posted earlier today, about an advanced topic called Macaulay duration… Read the rest

January 15, 2019July 13, 2019

Deconstructing the Mean Value Theorem, Part 2

*The Mean Value Theorem says there’s at least one point where the slope of the tangent line on a smooth curve equals the slope of the secant line between the endpoints.*

At its heart, the Mean Value Theorem is fairly intuitive. It essentially states that a smooth curve has at least one tangent line whose slope is equal to the

… Read the rest

January 11, 2019January 28, 2019

Financial Mathematics Fundamentals: Time Value of Money, Interest Rates, and Discount Factors

The word “discount” has the rare ability to cause peoples’ hearts to race for joy.

I certainly get excited when items are on sale, though I am wary of situations where the original price might be high to begin with.

The mathematics of discounts can be confusing for many people. I once had a student who was very fast at … Read the rest

January 10, 2019July 4, 2019

Financial Mathematics Tools: Substitutions, Quadratic Formula, Logarithms, and “Functional-Thinking”

Useful pre-university mathematics is not restricted to arithmetic, percentages, and basic algebra.

Functional-thinking is one key to doing many other useful things. Tools such as substitutions, the quadratic formula, and logarithms also come in handy.

These tools are used in engineering and science. For example, in the evaluation of useful integrals (such as those that come up in … Read the rest

January 8, 2019July 13, 2019

Deconstructing the Mean Value Theorem, Part 1

Visual interpretation of the Mean Value Theorem. — The Mean Value Theorem says there’s at least one point where the slope of the tangent line on a smooth curve equals the slope of the secant line between the endpoints.

Many mathematicians start chanting “MVT! MVT! MVT!” when they see the Mean Value Theorem in action. This is indeed because it is so valuable.

What does it mean … Read the rest

January 7, 2019March 4, 2019

Foundational Tools for Financial Mathematics: Timelines and Equations of Value

Improving your understanding of mathematics and its applications is a multifaceted process.

It is of utmost importance to become comfortable with abstract ideas, symbols, and the mental manipulation of these things. You should know the rules of algebra so well that they become automatic. Furthermore, visual representations of the concepts are often essential to seeing why facts are true and … Read the rest

January 3, 2019March 4, 2019

The Road Ahead

My plans for this blog are ambitious.

My main goal for Infinity is Really Big is to bring you excellence in mathematical content for your personal and professional growth.

YouTube-Related Content

As of the early January 2019, my YouTube channel, “Bill Kinney Math“, is moderately successful. It has over half a million views and over 4400 subscribers. The … Read the rest