function Archives - Infinity is Really Big

July 1, 2019September 20, 2019

High-Dimensional Linear Algebra

Visual Linear Algebra Online, Section 1.7

Image by Danilo Bueno from Pixabay

Many practical situations that require the use of linear algebra can involve hundreds or even thousands of unknowns. Modeling a national economy, optimizing the purchase of supplies, and managing flight schedules are prominent examples.

A vector quantity representing all the data in such a situation might therefore … Read the rest

March 22, 2019March 25, 2019

De Morgan’s Laws and Commutative Diagrams

New Videos: Videos #3 and #4 on Probability for Actuarial Exam 1/P

As I emphasized in my most recent post “Venn Diagrams and Probability Notation“, simple probability problems are often best solved with pictures and basic logic, but more complicated problems may require formulas.

We are definitely not at the point in my video series where more complicated … Read the rest

January 24, 2019January 28, 2019

New Video: Rebalancing a Bond Portfolio for a New Macaulay Duration

Rebalancing a portfolio is an important kind of financial planning action. It can be done to increase your rate of return or to change the susceptibility of the value of your investments to changes in yield rates.

For a coupon bond, the “duration” or “length” of the bond is a way to measure its susceptibility to … Read the rest

January 10, 2019July 4, 2019

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

The quadratic formula

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