My name is Valerie, and my pronouns are she/her. I have a passion for teaching math, and I especially love its applications. Math class seldom goes over applications, which is why many students see math as "boring" and "useless" until they see its everyday uses. In the future I plan to pursue a Ph.D. in applied mathematics to become a math professor, but for now I have this site to share what I can. I taught myself calculus in ninth grade and achieved a 5 on the Calculus BC exam. In tenth grade I started to tutor and began writing pages for this site. AP Physics C, which I took that year, inspired me to create pages dedicated to mathematical applications. I found a lot of gratification in learning physics with calculus applied, as doing so formulated a more complete understanding and introduced some applications that I write about now.
I built this website using HTML, CSS, and JavaScript. I used MathJax to display the equations. MathJax permits me to type LaTeX, but I've been limited because I cannot add packages to the code. Most of the graphs on this site were made using Desmos and some photoshop, but I've had to resort to external tools for animations and geometry—namely, Manim.
The problems on this site were all written by me. I will admit that some of them are made to be intentionally hard (mainly the last problems in a section set), so I wouldn't worry too much if there are a few you can't do. However, doing them is a great way to prepare for any tests because you'll have been exposed to potentially harder questions. And fun fact: one day I came up with about twenty extremely hard integrals—and now, looking back, I can barely do five of them! On some sections, there are probably about two or three problems that I couldn't do without referencing the answer key I made.
I follow these guidelines when I write. These styles are open to discussion, however; if you disagree and would like to propose an alternative, please contact me.
\((1)\) In a list of three or more items, a comma is required after the penultimate item in the series (this is more commonly known as the "Oxford Comma.") For example, a sentence such as I like A, B and C must instead be punctuated as I like A, B, and C.
\((2)\) A space must be inserted before a question mark if the last word is mathematical. For example, a question such as What is the value of \(d\)? must be rewritten as What is the value of \(d\) ? to ensure readability. However, a sentence such as For what values of \(k\) is \(f(x)\) continuous? does not warrant a space before the question mark because the last word is not mathematical.
\((3)\) Periods and commas are to be placed inside quotation marks, unless the last word of the quoted content is mathematical, in which case the punctuation mark must be placed outside. For example, the sentence We will call this value "\(x_{avg}\)," as shown by … is unreadable and may erect confusion. Therefore, it is best to rewrite the sentence as We will call this value "\(x_{avg}\)", as shown by … .
\((4)\) Lists should be numbered using LaTeX code. Parentheses must enclose the number, with the exception of exercise numbers.
\((5)\) For mathematical discussions, it is recommended to add emphasis by using the phrases in order to and in order for in place of to and for, respectively. In conditional clauses, it is also recommended to add the word then. For example, it is recommended to write If \(\sum |a_n|\) converges, then so does \(\sum a_n\) instead of If \(\sum |a_n|\) converges, so does \(\sum a_n\).