Why Are People That Are Good at Math Good at Art and Medicine?

Author: David Chasteen-Boyd

It sometimes seems like there is a pre-medical student everywhere you plough at UAB. Pre-meds are one of the nearly motivated (and sleep-deprived) groups of students on campus. The pre-med curriculum expects students to be very well-rounded and is not easy by whatsoever standard. These students take various and often difficult classes including general and organic chemistry, general physics, biology, and English language literature. Withal, from my feel being friends with and tutoring many pre-med students, the subject area they seem to dislike about is math—specifically calculus and statistics. One of the most common complaints I hear regarding these fields of math is "Why do I need to learn this? When am I always going to utilise this as a medico?". I'd like to take the time to answer these questions for all of the pre-meds wondering the same thing, and present an argument for why upper-level math classes (past Calculus I and Statistics) are useful in medicine.

The more immediate reasons that math is useful to future physicians are axiomatic in the pre-med curriculum itself. Starting time, many medical schools crave either calculus or statistics (or both) to be considered for access. The University of California at Berkeley Career Heart has compiled a list of medical schools in the U.S. and Canada and their admissions requirements in different subject areas.¹ Out of 64 schools whose requirements are given, 40 schools require—and the remaining 24 recommend—at to the lowest degree 1 semester of college-level math. Some medical schools specified math courses that they want incoming students to have taken. Twenty-six of the schools recommend or require that students take calculus and nine of the schools require or recommend statistics. So, only to go into medical schoolhouse, pre-meds frequently have to take calculus or statistics.

Additionally, almost every medical school requires students to accept physics as well as general and organic chemistry, non to mention the fact that physics is well represented on the Medical College Admission Test (MCAT). These fields are strongly calculus-based. Physics is almost completely derived from calculus, and calculus was really developed by Isaac Newton to further the study of physics. In a postal service on studentdoctor.internet, a prospective md asked nigh the usefulness of math for physicians. Many explanations were given, only the general consensus was that an agreement of calculus leads to better comprehension of chemistry and physics.² Given that these subjects found a significant portion of the MCAT, information technology would benefit any pre-med student to acquire calculus.

From a more abstract perspective, calculus offers new ways of thinking that are quite useful to a medical practitioner. Calculus is the written report of both the infinitesimally small and the infinitely big. Differential calculus studies the very small; derivatives wait at the behavior of a function at ii points that are very close to each other and how that function changes between those two points (or more but, derivatives are a style to correspond a rate of change). This forces one to consider what kinds of changes happen on an infinitesimally small scale. These kinds of changes are common in biology and medicine; tiny changes in medicine (such every bit pH, drug concentration, etc.) can effect large changes in the wellness of a patient. Integral calculus (and the more general field of infinite series) is concerned with the very large; integrals are based on adding up an infinite number of small-scale pieces to yield a bigger picture. In medicine, this leads to the ability to call up of the body as the sum of many smaller pieces—namely the different systems, organs, tissues, etc.—and to consider their effects. Overall, the study of variations and how different variables irresolute can modify an overall system has useful applications in medicine. This is exactly the function of calculus. For example, calculus was used to develop the Cockroft-Gault equation, which determines the advisable drug dosage for patients with sure kidney diseases based on the level of creatinine in their claret. Equations like this are invaluable to physicians and could not exist without an understanding of calculus.³

In improver to Calculus I and Two, at that place are many college-level math classes that are useful in the study of medicine, especially to those who wish to acquit medical enquiry. 2 of these are multivariate calculus and differential equations. Multivariate calculus (called Calculus Iii here at UAB) studies the awarding of derivatives and integrals to functions of more ane variable. The dependent variable, z, can depend on two independent variables, ten and y (but this can be hands expanded to a role that depends on whatsoever number of variables). For example, one could study the stability of a novel drug commitment organisation (dependent variable, z) changes in response to variations in pH and temperature (independent variables, x and y). Multivariate equations are more than representative of reality, and they forcefulness one to consider the furnishings of many unlike variables on a variable of interest. It is rare in medicine to discover a cistron that depends solely on a single variable.  To consider a applied application of this manner of thinking, it has been shown that high stress in individuals tin weaken the allowed system.  So, stressed individuals can be more probable to get sick.  If a patient comes into a clinic with something every bit generic equally the influenza, doctors may need to consider treatments for causes other than just the virus that is infecting their patient.  Counseling or other stress-reduction techniques may also improve the patient's long term wellness.  Seeing how multiple variables are contributing to a particular situation tin can be a useful skill for clinicians.

Differential equations involve equations that contain both a function and its derivatives. I of the simplest differential equations is displayed below.

This kind of equation may at first seem petty. What is so important about an equation that contains a derivative? Information technology turns out that virtually every existent-globe organisation tin can be modelled by differential equations. For example, the FitzHugh-Nagumo equations (and the more complex Hodgkin-Huxley equations) are a system of differential equations that are used to model the depolarization of neuronal or cardiac cell membranes.^five The developers of the Hodgkin-Huxley model were awarded the Nobel Prize in Physiology or Medicine for their work on the equations.^{half dozen} These equations are useful to medical researchers because they can be used to study the function of cardiac cells nether dissimilar stimuli, and past extension, to report the mechanisms of certain heart diseases.

While calculus has many more than applications in medicine that could be discussed, it is also of import to discuss how other fields of math are useful to physicians. Going back to high school, an understanding of algebra and proportions, known as functional numeracy, is vital to practicing medicine. Doctors prescribe drugs on a daily basis, and at that place is no ane-size-fits-all dose of a particular drug. Doses are based on many factors, such as a patient's weight, BMI, health conditions, etc. Calculating the correct dosage can involve determining the period rate of a drug that is delivered intravenously, how frequently a patient should take a certain pill, and how large of a pill to requite the patient. These questions tin can be answered using algebra and ratios based on standardized per-weight formulas.^four Additionally, feel with math (and physics and chemical science) leads to an understanding of what results are reasonable. If you take taken physics and chemistry, you have probably calculated an absurdly high or low number as the solution to some problem. Y'all likely had a gut feeling that the reply was wrong and double-checked your work. Experience in the field can pb to an intuition for the reasonability of an answer, and exercise problems in math (and other) classes may bolster one'south level of experience.^vii

Statistics is applied to every area of the sciences, including medicine. Inquiry is constantly being done into many different aspects of medicine, and every bit a result the practice of medicine is constantly adapting based on emerging inquiry. In lodge to sympathize—and more importantly, critically clarify—the results and data assay sections of medical inquiry manuscripts, physicians need a strong groundwork in statistics. It is not uncommon for medical research manuscripts to study improper statistics, unsupported conclusions, and incorrect report designs.^viii A deep agreement of statistics is necessary for physicians to identify well-designed studies and properly analyzed information. With this skill, a physician can identify which manuscripts comprise data disarming enough to cause them to change their practice of medicine, and which conclusions are the results of poorly designed studies or inappropriate data analysis.

An understanding of calculus is also useful for analyzing the processes used to gather and filter information in medical manuscripts. Additionally, knowledge of these techniques can aid in the design and improvement of clinical studies. Dr. Mary Tai published a manuscript that described a "novel" method of measuring the surface area under a glucose tolerance curve.⁹ Glucose tolerance tests are used to diagnose conditions such as diabetes, insulin resistance, and others related to insulin metabolism. The area nether a glucose tolerance curve is a useful measure of glucose excursion.¹⁰ Dr. Tai's proposed formula for calculating the surface area under a glucose tolerance curve (which she named Tai's method) involves taking the curve, splitting information technology into an advisable number of intervals, and approximating the area in one interval every bit a trapezoid where the height of the trapezoid on either side of the interval is equal to the value of the glucose tolerance curve on either side of the interval. Anyone who has taken calculus will recognize this equally the trapezoid rule for approximating definite integrals, which has been in use since as early as 350 BCE.¹¹ In other words, Dr. Tai reinvented a well-known numerical integration method, believing it to be a novel concept. She also validated this method by comparison the results of using her method to a "standard" area of the bend; she obtained her standard by cartoon the curve on graph paper and counting the number of squares that were underneath the curve. This is clearly an inaccurate method of creating a control. Though this anecdote is amusing, it also serves as an example of why understanding calculus and statistics is vital to physicians, and especially to medical researchers. Other examples of calculus-based methods used to analyze medical data include image processing methods used to remove unwanted noise and objects from medical images and the Fourier transform, which tin remove noise from ECG and other signals.

Calculus and statistics are used in the medical profession in fields ranging from measuring kidney function to analyzing medical images to diagnosing diabetes. Clearly, mathematics is vital to the medical profession. A deep understanding of mathematics will ameliorate a pre-medical student's performance in undergraduate scientific discipline classes and on the MCAT.  Additionally, having a familiarity with these fields of math volition amend his or her practise of medicine post-medical school.

References

1. University of California at Berkeley Career Center. "2015 Medical Schoolhouse Math, English, Biochemistry & Psych/Soc Requirements." (2015): Spider web. 21 December. 2016
2. "Do Doctors have to be Good in Math????" (2000-2015): studentdoctor.internet. Web. 23 Dec. 2016.
3. "Cockcroft-Gault Formula." Kidney.org. The National Kidney Foundation. Web. 23 Dec. 2016.
4. Natasha Glydon. "Medicine and Math." Mathcentral.uregina.ca. Math Central. Web. 22 Dec. 2016.
5. Hodgkin, A. L., and A. F. Huxley. "A Quantitative Clarification of Membrane Current and Its Awarding to Conduction and Excitation in Nervus."The Journal of Physiology 117.iv (1952): 500–544. Impress.
6. "The Nobel Prize in Physiology or Medicine 1963".Nobelprize.org. Nobel Media AB 2014.Web. 24 Dec 2016. http://www.nobelprize.org/nobel_prizes/medicine/laureates/1963/
7. Neil J. Nusbaum, "Mathematics Training for Medical School: Exercise All Premedical Students Need Calculus?"Teaching and Learning in Medicine,18(2), (2006): 165–168.
8. Strasak, Alexander M.; Zaman, Qamruz; Pfeiffer, Karl P.; Göbel, Georg; Ulmer, Hanno."Statistical errors in medical research – a review of common pitfalls." Swiss Medical Weekly. 137 (2007): 44-49. Web. 23 Dec. 2016.
9. Tai, Mary M. "A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves." Diabetes Care. 17(two). (1994): 152-154. Web. 22 Dec. 2016.
10. Sakaguchi, One thousand., Takeda, K., Maeda, M. et al. Diabetol Int (2016) vii: 53.doi:ten.1007/s13340-015-0212-4
11. 1000. Ossendrijver. "Aboriginal Babylonian astronomers calculated Jupiter's position from thearea under a time-velocity graph."Science (2016). Web. 23 December. 2016.

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Source: https://www.uab.edu/inquiro/issues/current-issue/why-future-physicians-should-study-math

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