## Mathematics is not a spectator sport (How to study Maths for Humanities students)

Studying Mathematics is totally different from studying Humanities, this is the reason why humanities students often don’t do well in maths. But with the right studying techniques (i.e. practising doing mathematics), humanities students can be very good at maths. Together with their creativity and good memory, humanities students have the potential to achieve the top grades in maths exams.

I have taught Pure Literature students and found that they definitely have the potential to do well in Maths once they learn the correct method of mathematical studying and thinking, and how to approach solving Maths questions.

One of the top mathematical physicists, Edward Witten, majored in history and minored in linguistics! (http://en.wikipedia.org/wiki/Edward_Witten)

# Mathematics is not a spectator sport

Even if you understand every word in lecture and in the textbook, the only way to really learn mathematics is by doing mathematics.  Sometimes this means doing even more than the assigned problems.  (See “time committment” above.)  This is how to avoid the common pitfall of “understanding everything in class but blanking out on the exams.

I realize this isn’t welcome advice, and I admit that I haven’t always followed it myself.  But in years of teaching (and 20+ years of learning) mathematics I haven’t found any shortcut.

## Maths Skills to be a Doctor

Doctor and Lawyer are the top two favourite careers in Singapore. Do doctors need to use Maths? Read the below to find out.

Even if Maths is not directly needed, the logical thinking skills learnt in Mathematics will definitely be of great use. 🙂

I am not a medical doctor, but my two younger siblings are medical students, and the Mathematical knowledge and thinking skills have definitely helped them in their medical studies.

Functional numeracy is as essential to an aspiring medical professional as functional literacy. As a physician, perhaps the most important mathematical skills you will need are:

1. Basic mathematical knowledge sufficient to calculate drug doses, concentrations, etc.

2. An understanding of the core statistical concepts most commonly represented in the medical literature.

3. Knowledge of algebra to understand calculations of acid–base status, etc.

4. Ability to appreciate whether or not results are mathematically plausible.    (Nusbaum, 2006)

The careful logical reasoning that is necessary for the study of mathematics is an essential element of clinical reasoning. Although you do not need higher mathematics to get through medical school, you will need the ability to manipulate numbers, including fractions, ratios, powers of 10 and logarithms. You will also need a basic understanding of probability, graphs and simple algebra. You will need to rearrange equations and convert between units of measure.

It’s often unclear from your interactions with a doctor how much math she is using in order to treat you. While not all doctors have to use math as directly and frequently as engineers do, all of them must understand the complex mathematical equations that inform different medical treatments in order to administer treatments correctly.

## Dosages and Half-Life

One of the most common ways in which doctors use mathematics is in the determination of medicine prescriptions and dosages. Doctors not only have to use basic arithmetic to calculate what dosage of a particular drug will be effective for your height and body type over a specific period of time, they will also have to be aware of the medicine’s cycle through the body and how the dosage of one drug compares with the dosage of a similar type of drug. Sometimes doctors have to use calculus to figure out the right dosage of a drug. Calculus is the study of how changing variables affect a system. In the human body, the kidney processes medicine. However, people’s kidneys are at varying levels of health. Doctors can designate the kidney as a changing function in a calculus equation known as the Cockroft-Gault equation. This equation uses the level of creatine in a patient’s blood to find the level of the kidney’s functioning, which allows the doctor to determine the appropriate dose.

## Cancer Treatment

When a doctor administers radiation therapy to a cancer patient, the radiation beams have to cross each other at specific angles, so that they harm the cancerous tumor without harming the surrounding healthy tissue. The precise numbers for these angles must be calculated mathematically. Cancer tends to respond to any drug by mutating so that its DNA is no longer affected by that drug. Oncologists and medical scientists have decided to target cancerous tumors with many different kinds of drugs at once so that the cancer is unable to respond adequately. They use complex mathematical models that plot the speed and timing of the cancer’s different mutations to figure out what combinations and dosages of different drugs should be used.

## Medical Images and Tests

Doctors in medical imaging use two-dimensional images of a patient’s body taken from thousands of angles to create a three-dimensional image for analysis. Determining what angles should be used and how they will fit together requires mathematics. Medical researchers who study disease will analyze the mathematical dimensions of these images. Neurologists who run EEGs on patients to measure their brain waves must add and subtract different voltages and use Fourier transforms to filter out signal static. Fourier transforms are used to alter functions in calculus.

## Treatment Research

Medical scientists working with cardiologists use differential equations to describe blood flow dynamics. They also build sophisticated computer models to find the ideal size of an artificial aorta and where to place it in an infant pending a heart transplant. Doctors have to read medical journals to keep up on the latest scientific findings for the benefit of their patients. In addition to describing the calculus used to model health conditions, medical journal studies also make heavy use of statistics and probability to describe the health conditions of whole populations and the likelihood that different treatments will be effective.

## The Key To Career Success

“The essence of mathematics is not to make simple things complicated, but to make complicated things simple.” ~ Stan Gudder, Mathematician

Math, at its core, is about solving problems — about breaking a challenge into its basic elements to be investigated, tested, manipulated and understood. Math can give you the tools to find a winning formula. And, it can create the path to your career.

Math is the key to unlocking possibilities. It frees you up to think creatively about solutions and to focus your attention on what truly matters at the end of the day.

Finally, math empowers you to be a better leader and to remain open to new ideas. It sparks creativity and learning. It gives you confidence and conviction to say “YES!” when you’re asked to take on a new challenge. It helps you attract and energize the people you hire to help you.  In a marketplace that’s moving so fast, it’s important to constantly listen, learn, analyze and formulate new ways to serve customers.  Math provides the foundation for doing just that.

Want to succeed? It’s simple … math.

## How to avoid Careless Mistakes for Maths?

Many parents have feedback to me that their child often makes careless mistakes in Maths, at all levels, from Primary, Secondary, to JC Level. I truly empathize with them, as it often leads to marks being lost unnecessarily. Not to mention, it is discouraging for the child.

Also, making careless mistakes is most common in the subject of mathematics, it is rare to hear of students making careless mistakes in say, History or English.
Fortunately, it is possible to prevent careless mistakes for mathematics, or at least reduce the rates of careless mistakes.

From experience, the ways to prevent careless mistakes for mathematics can be classified into 3 categories, Common Sense, Psychological, and Math Tips.

Common Sense

1. Firstly, write as neatly as possible. Often, students write their “5” like “6”. Mathematics in Singapore is highly computational in nature, such errors may lead to loss of marks. Also, for Algebra, it is recommended that students write l (for length) in a cursive manner, like $\ell$ to prevent confusion with 1. Also, in Complex Numbers in H2 Math, write z with a line in the middle, like Ƶ, to avoid confusion with 2.
2. Leave some time for checking. This is easier said than done, as speed requires practice. But leaving some time, at least 5-10 minutes to check the entire paper is a good strategy. It can spot obvious errors, like leaving out an entire question.

Psychological

1. Look at the number of marks. If the question is 5 marks, and your solution is very short, something may be wrong. Also if the question is just 1 mark, and it took a long time to solve it, that may ring a bell.
2. See if the final answer is a “nice number“. For questions that are about whole numbers, like number of apples, the answer should clearly be a whole number. At higher levels, especially with questions that require answers in 3 significant figures, the number may not be so nice though. However, from experience, some questions even in A Levels, like vectors where one is suppose to solve for a constant $\lambda$, it turns out that the constant is a “nice number”.

Mathematical Tips

Mathematical Tips are harder to apply, unlike the above which are straightforward. Usually students will have to be taught and guided by a teacher or tutor.

1. Substitute back the final answer into the equations. For example, when solving simultaneous equations like x+y=3, x+2y=4, after getting the solution x=2, y=1, you should substitute back into the original two equations to check it.
2. Substitute in certain values. For example, after finding the partial fraction $\displaystyle\frac{1}{x^2-1} = \frac{1}{2 (x-1)}-\frac{1}{2 (x+1)}$, you should substitute back a certain value for x, like x=2. Then check if both the left-hand-side and right-hand-side gives the same answer. (LHS=1/3, RHS=1/2-1/6=1/3) This usually gives a very high chance that you are correct.

Thanks for reading this long article! Hope it helps! 🙂

I will add more tips in the future.

## Recommended Maths Book:Math Doesn’t Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail

This book is a New York Times Bestseller by actress Danica McKellar, who is also an internationally recognized mathematician and advocate for math education. It should be available in the library. Hope it can inspire all to like Maths!