MedicineandMath

**Natasha Glydon**

Both doctors and nurses use math every day while providing health care for people around the world. Doctors and nurses use math when they write prescriptions or administer medication. Medical professionals use math when drawing up statistical graphs of epidemics or success rates of treatments. Math applies to x-rays and CAT scans. Numbers provide an abundance of information for medical professionals. It is reassuring for the general public to know that our doctors and nurses have been properly trained by studying mathematics and its uses for medicine.

Prescriptions and Medication

Regularly, doctors write prescriptions to their patients for various ailments. Prescriptions indicate a specific medication and dosage amount. Most medications have guidelines for dosage amounts in milligrams (mg) per kilogram (kg). Doctors need to figure out how many milligrams of medication each patient will need, depending on their weight. If the weight of a patient is only known in pounds, doctors need to convert that measurement to kilograms and then find the amount of milligrams for the prescription. There is a very big difference between mg/kg and mg/lbs, so it is imperative that doctors understand how to accurately convert weight measurements. Doctors must also determine how long a prescription will last. For example, if a patient needs to take their medication, say one pill, three times a day. Then one month of pills is approximately 90 pills. However, most patients prefer two or three month prescriptions for convenience and insurance purposes. Doctors must be able to do these calculations mentally with speed and accuracy.

Doctors must also consider how long the medicine will stay in the patient’s body. This will determine how often the patient needs to take their medication in order to keep a sufficient amount of the medicine in the body. For example, a patient takes a pill in the morning that has 50mg of a particular medicine. When the patient wakes up the next day, their body has washed out 40% of the medication. This means that 20mg have been washed out and only 30mg remain in the body. The patient continues to take their 50mg pill each morning. This means that on the morning of day two, the patient has the 30mg left over from day one, as well as another 50mg from the morning of day two, which is a total of 80mg. As this continues, doctors must determine how often a patient needs to take their medication, and for how long, in order to keep enough medicine in the patient’s body to work effectively, but without overdosing.

The amount of medicine in the body after taking a medication decreases by a certain percentage in a certain time (perhaps 10% each hour, for example). This percentage decrease can be expressed as a rational number, 1/10.Hence in each hour, if the amount at the end of the hour decreases by 1/10 then the amount remaining is 9/10 of the amount at the beginning of the hour. This constant rational decrease creates a geometric sequence. So, if a patient takes a pill that has 200mg of a certain drug, the decrease of medication in their body each hour can be seen in the folowing table. The **Start** column contains the number of mg of the drug remaining in the system at the start of the hour and the **End** column contains the number of mg of the drug remaining in the system at the end of the hour.

Hour | Start | End |
---|---|---|

1 | 200 | 9/10 x 200 = 180 |

2 | 180 | 9/10 x 180 = 162 |

3 | 162 | 9/10 x 162 = 145.8 |

. | . | . |

The sequence of numbers shown above is geometric because there is a common ratio between terms, in this case 9/10. Doctors can use this idea to quickly decide how often a patient needs to take their prescribed medication.

Ratios and Proportions

Nurses also use ratios and proportions when administering medication. Nurses need to know how much medicine a patient needs depending on their weight. Nurses need to be able to understand the doctor’s orders. Such an order may be given as: 25 mcg/kg/min. If the patient weighs 52kg, how many milligrams should the patient receive in one hour? In order to do this, nurses must convert micrograms (mcg) to milligrams (mg). If 1mcg = 0.001mg, we can find the amount (in mg) of 25mcg by setting up a proportion.

By cross-multiplying and dividing, we see that 25mcg = 0.025mg. If the patient weighs 52kg, then the patient receives 0.025(52) = 1.3mg per minute. There are 60 minutes in an hour, so in one hour the patient should receive 1.3(60) = 78mg. Nurses use ratios and proportions daily, as well as converting important units. They have special “shortcuts” they use to do this math accurately and efficiently in a short amount of time.

Numbers give doctors much information about a patient’s condition. White blood cell counts are generally given as a numerical value between 4 and 10. However, a count of 7.2 actually means that there are 7200 white blood cells in each drop of blood (about a microlitre). In much the same way, the measure of creatinine (a measure of kidney function) in a blood sample is given as *X *mg per deciliter of blood. Doctors need to know that a measure of 1.3 could mean some extent of kidney failure. Numbers help doctors understand a patient’s condition. They provide measurements of health, which can be warning signs of infection, illness, or disease.

Body Mass Index

In terms of medicine and health, a person’s Body Mass Index (BMI) is a useful measure. Your BMI is equal to your weight in pounds, times 704.7, divided by the square of your height in inches. This method is not always accurate for people with very high muscle mass because the weight of muscle is greater than the weight of fat. In this case, the calculated BMI measurement may be misleading. There are special machines that find a person’s BMI. We can find the BMI of a 145-pound woman who is 5’6” tall as follows.

First, we need to convert the height measurement of 5’6” into inches, which is 66”. Then, the woman’s BMI would be:

This is a normal Body Mass Index. A normal BMI is less than 25. A BMI between 25 and 29.9 is considered to be overweight and a BMI greater than 30 is considered to be obese. BMI measurements give doctors information about a patient’s health. Doctor’s can use this information to suggest health advice for patients. The image below is a BMI table that gives an approximation of health and unhealthy body mass indexes.

Image reproduced with permission of Health Canada

CAT Scans

One of the more advanced ways that medical professionals use mathematics is in the use of CAT scans. A CAT scan is a special type of x-ray called a Computerized Axial Tomography Scan. A regular x-ray can only provide a two-dimensional view of a particular part of the body. Then, if a smaller bone is hidden between the x-ray machine and a larger bone, the smaller bone cannot be seen. It is like a shadow.

Image reproduced with permission of NeuroCognition Laboratory

It is much more beneficial to see a three dimensional representation of the body’s organs, particularly the brain. CAT scans allow doctors to see *inside* the brain, or another body organ, with a three dimensional image. In a CAT scan, the x-ray machine moves around the body scanning the brain (or whichever body part is being scanned) from hundreds of different angles. Then, a computer takes all the scans together and creates a three dimensional image. Each time the x-ray machine makes a full revolution around the brain, the machine is producing an image of a thin slice of the brain, starting at the top of the head and moving down toward the neck. The three-dimensional view created by the CAT scan provides much more information to doctors that a simple two-dimensional x-ray.

Mathematics plays a crucial role in medicine and because people’s lives are involved, it is very important for nurses and doctors to be very accurate in their mathematical calculations. Numbers provide information for doctors, nurses, and even patients. Numbers are a way of communicating information, which is very important in the medical field.

Another application of mathematics to medicine involves a lithotripter. This is a medical device that uses a property of an ellipse to treat gallstones and kidney stones. To learn more, visit the **Lithotripsy** page.

## FAQs

### Can I still be a doctor if I'm bad at math? ›

You don't have to be a good in math to pursue medicine. The most important thing that you have to think about is how much dedication are you willing to give when you pursue that career. **Being a doctor does not require being good in math but would require commitment.**

**Do you need to be good at math to study medicine? ›**

While calculus has many more applications in medicine that could be discussed, it is also important 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.**

**What is the hardest math class in school? ›**

What is the Hardest Math Class in High School? In most cases, you'll find that **AP Calculus BC or IB Math HL** is the most difficult math course your school offers. Note that AP Calculus BC covers the material in AP Calculus AB but also continues the curriculum, addressing more challenging and advanced concepts.

**What is the hardest math topic in college? ›**

**Calculus** is, according to Wikipedia, “ … the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.” BUT, don't give up all hope if you need this class for your degree.

**What doctor uses the least math? ›**

Medical Transcriptionists

Medical transcription is one of the medical jobs with the least math involved. Medical transcription is an interesting, yet challenging career path that requires skills such as being able to concentrate intently and having solid healthcare knowledge.

**What is the highest math you need to be a doctor? ›**

Most medical schools want college students to take a full year of **calculus** in college.

**Is there calculus in med school? ›**

The majority of medical schools (M.D. and D.O.) with a math requirement will look for between one and two semesters of math. **Most of them would expect a semester of calculus** and a semester of statistics. No health professions schools require multivariable calculus.

**What medical degree doesn t require math? ›**

- Allied Health.
- Medical Assisting.
- Medical Billing & Coding.
- Occupational Therapy.
- Phlebotomy.
- Physical Therapy Assisting.
- Radiologic Technology.
- Surgical Technology.

**How many med schools require calculus? ›**

A: **Over 50** medical schools require one or two semesters of mathematics (college math, calculus, and/or statistics).

**What is the most failed high school math class? ›**

**Algebra I** is the single most failed course in American high schools. Thirty-three percent of students in California, for example, took Algebra I at least twice during their high school careers. And students of color or those experiencing poverty are overrepresented in this group.

### What is the hardest pre-med class? ›

While this question is subjective, the hardest pre-med major is considered **organic chemistry**.

**Did Bill Gates pass math 55? ›**

**Bill Gates took Math 55**.

To get a sense of the kind of brains it takes to get through Math 55, consider that Bill Gates himself was a student in the course. (He passed.) And if you'd like to sharpen your brain like Microsoft's co-founder, here are The 5 Books Bill Gates Says You Should Read.

**What's the easiest math to take in college? ›**

**What is the Easiest Math Class in College?**

- Statistics: Statistics is a branch of mathematics dealing with the collection, analysis, and interpretation of numerical data. ...
- Finite Math: Finite math refers to a variety of math courses that do not involve calculus.

**What is harder than calculus? ›**

In general, statistics is more vast and covers more topics than calculus. Hence, it is also perceived to be more challenging. Basic or entry-level statistics is much easier as compared to basic level calculus. **Advance level statistics** is much much harder than advanced level calculus.

**What is the hardest doctor to study? ›**

**Based on our comprehensive analysis, the top most competitive specialties are as follows:**

- Plastic Surgery.
- ENT.
- Dermatology.
- Orthopedic Surgery.
- Neurosurgery.
- Thoracic Surgery.
- Urology.
- Vascular Surgery.

**What is the simplest type of doctor? ›**

1. **Family Medicine**. Family medicine practitioners are trained in pediatrics and adult care (including gynecology and gastroenterology) so that they can treat every member of the family. Their work involves comprehensive care and requires an understanding of most ailments.

**What majors don t require calculus? ›**

**The following majors do not require Calculus**

- Anthropology.
- Art and Art History.
- Classics.
- Communication.
- English.
- Environmental Studies.
- Ethnic Studies.
- History.

**What math is used in medicine? ›**

Healthcare professionals use **basic arithmetic** every day, and simple geometry and algebra less often.

**What kind of math do surgeons use? ›**

In their professional life, thoracic surgeons could use **elementary mathematics** as arithmetic (regarded as the most immediately useful parts of mathematics). A surgeon can count, performs elementary arithmetic, and even understands simple graphs and statistics.

**Do doctors ever use calculus? ›**

In order for doctors to prescribe the correct dosage of a drug and provide a regimen for treatment (ie., “take 2 capsules twice a day”), the drug's concentration over time must be tracked. This prevents under and over-dosing. The way that a drug's concentration over time is calculated is using calculus!

### Can I get into med school if I fail calculus? ›

**Medical schools accept students with any undergraduate major, as long as you also take the required courses that would not normally be included in a math major**.

**Is there a lot of math in medicine? ›**

**Medical professionals use math when drawing up statistical graphs to show success rates of treatments and other large data points**. All graphs, equations, statistics, and general maths we learn at school help us understand important aspects of human and veterinary medicine, biology, and science.

**Do I need calculus for MCAT? ›**

The MCAT is a conceptual exam that requires little mathematical computation. Any such requirements are based only on fundamental mathematical concepts, which include arithmetic, algebra, and trigonometry. **There is no calculus involved**.

**Do med schools like math majors? ›**

According to this data, there are three major groups—humanities, math and statistics, and physical sciences—that **enjoy higher admissions rates than others**. In fact, these are the only three groups (aside from biological sciences) that get into medical school at a rate greater than 40 percent.

**Is there a lot of math in surgical tech? ›**

Complex math isn't part of the day-to-day for the typical surgical technologist. **Simple calculations or unit conversion may be required, but no further advanced math skills will be commonly needed**.

**What career requires the least amount of math? ›**

**15 High-Paying Jobs That Don't Require Too Much Math**

- Marketing manager. Marketing managers may have to deal with a budget on occasion, but their main purpose is to create advertising and marketing for clients. ...
- Transportation inspector. ...
- Technical writer. ...
- Historian. ...
- Web developer. ...
- Dental hygienist. ...
- Lawyer. ...
- Psychologist.

**Can I get into med school with all C's? ›**

**Schools won't think you can't handle medical school because you got a C**. More likely, they will look into where you've gone from there. Some students retake the classes early on.

**Do you need Calc to be a doctor? ›**

**At most, medical schools will require a combination of calculus and statistics**, so we'd recommend that you stick with your AP Calc credit plus a semester of statistics later on.

**Is calculus required for Harvard medical school? ›**

Mathematics. Pathways **applicants are encouraged to complete a one-year mathematics sequence that includes calculus and statistics, preferably biostatistics**.

**Which is harder algebra or calculus? ›**

**Calculus is the hardest mathematics subject** and only a small percentage of students reach Calculus in high school or anywhere else. Linear algebra is a part of abstract algebra in vector space. However, it is more concrete with matrices, hence less abstract and easier to understand.

### What is the hardest high school class in America? ›

- Physics 1. As one of the hardest high school classes, this course includes not only algebra but also scientific inquiry and physics. ...
- Environmental Science. ...
- Chemistry. ...
- U.S. Government and Politics. ...
- U.S. History. ...
- Human Geography. ...
- European History. ...
- Statistics.

**What is the easiest math in high school? ›**

Which math classes are the easiest? According to a large group of high-schoolers, the easiest math class is **Algebra 1**. That is the reason why most of the students in their freshman year end up taking Algebra 1. Following Algebra 1, Geometry is the second easiest math course in high school.

**Is a 3.7 GPA good for pre-med? ›**

Admissions experts advise aspiring medical school students to aim for a GPA of **3.5 or higher**.

**What is a bad pre-med GPA? ›**

What is considered a low GPA for medical school? Many medical schools have a cut-off for GPAs **below 3.0**. The average GPA at most MD medical schools ranges from about 3.7 to 3.9. The average GPA at most DO medical schools ranges from about 3.4 to 3.6.

**What year is the most difficult in med school? ›**

The **third year** of medical school is by far the hardest, current and former med students will almost always agree.

**What is the highest math class at Harvard? ›**

**Math 55** is a two-semester long first-year undergraduate mathematics course at Harvard University, founded by Lynn Loomis and Shlomo Sternberg. The official titles of the course are Honors Abstract Algebra (Math 55a) and Honors Real and Complex Analysis (Math 55b).

**What is the hard math class at Harvard? ›**

**Math 55** is a two-semester long freshman undergraduate mathematics course at Harvard University founded by Lynn Loomis and Shlomo Sternberg. The official titles of the course are Studies in Algebra and Group Theory (Math 55a) and Studies in Real and Complex Analysis (Math 55b).

**What is the lowest level college math? ›**

What is college-level math? Entry-level math in college is considered the stepping stone to more advanced math. **Algebra 1, trigonometry, geometry, and calculus 1** are the basic math classes. Once you have successfully navigated through these courses, you can trail blazed through more advanced courses.

**What is the easiest major with no math? ›**

**Here's a list of 16 college majors that don't rely on math for you to consider:**

- Anthropology. Anthropology is the study of humans. ...
- Linguistics. ...
- Theology. ...
- History. ...
- Psychology. ...
- Sociology. ...
- Occupational therapy. ...
- Culinary arts.

**What should I study in college if I don't like math? ›**

What Should I Major in if I Hate Math? **Management, business, research, or finance** positions often don't require algebra or calculus, but they may require some skill in statistics or other computational skills.

### Do most students fail calculus? ›

Those concerns were heightened given significant declines in recent standardized math test scores for K-12 California students, most of whom spent 2020-21 in distance learning. CSU Bakersfield reports that **35.5% of students on average have been failing or withdrawing from Calculus 1 since 2018**.

**Do colleges prefer calculus or statistics? ›**

But for many other students, calculus isn't the math course that will most help them—the right course often is statistics. But **most admissions counselors have favored calculus (in many cases informally)**, the report says, and that hurts students.

**What is the most complex branch of math? ›**

**Calculus**

One of the most complex and highly advanced branches of mathematics, which in fact itself has levels to it, be it Pre-calculus, advanced calculus, Accelerated Multivariable Calculus, differential calculus, integral calculus, etc.

**What is the toughest degree in the world? ›**

**What are the hardest degrees in the world?**

**Ranked by Experts**

- Chartered Accountancy.
- Astrophysics.
- Quantum Mechanics.
- Law.
- Aerospace/ Aeronautical Studies, Engineering.
- Biomedical Studies, Neurosciences, Biochemistry.
- Nursing.
- Dentistry, Medicine.

**What is the lowest grade Harvard accepts? ›**

After being admitted with a 3.0 or higher grade-point average (GPA), you must maintain a cumulative GPA of 2.0 to be considered in good academic standing. **If your GPA falls below 2.0**, you are in poor academic standing.

**Is MIT harder than Harvard? ›**

In terms of standardized test scores, MIT students have slightly higher averages, with an SAT score of 1520 and an ACT score of 35, compared with Harvard's averages of 1480 and 35. Overall, these slight differences are nominal, meaning that **both schools are extremely hard to get into**.

**Can you be bad at math and still go to college? ›**

Sure! Most colleges will have you take aptitude tests in various subjects before you enter. **If you do poorly on the math test, they'll have you take one or more basic catch-up courses in math.**

**Can people with bad grades become doctor? ›**

Getting into medical school with a low GPA is something that many students think is impossible. But that's not the case at all. In fact, **med schools accept students with a low GPA every year**.

**What jobs do you not need to be good at math? ›**

**20 high-paying jobs that don't require math**

- Compliance manager.
- Marketing manager.
- Music teacher.
- Historian.
- Recruitment manager.
- Art director.
- Web developer.
- Documentation manager.

**Can I be a doctor if I'm not good at science? ›**

All “evidence” in medicine is based on scientific research, and a great deal of medicine requires scientific thinking. If you are not good at science and math, **medical school might be a very bad choice**.

### What degree requires no math? ›

If you would like to avoid math altogether, you may consider **human services jobs with a strong psychology, counseling, or social welfare component**. Jobs in writing, publishing, public relations, advertising, and communications also require virtually no math at all.

**Is math the hardest major in college? ›**

Not surprisingly, **mathematics takes second place for hardest college major**. A bachelor's in math may seem a bit generic, but it's actually quite flexible. Employers everywhere are seeking individuals who think independently, creatively and critically, and math students do exactly that.

**Can you pass college with dyscalculia? ›**

**Dyscalculia or math learning disability/disorder will prevent you from meeting minimum quantitative reasoning requirements at the college level**. For liberal arts majors, this usually means passing a class in College Algebra or Finite Math.

**What GPA is too low for med school? ›**

What is considered a low GPA for medical school? Many medical schools have a cut-off for GPAs **below 3.0**. The average GPA at most MD medical schools ranges from about 3.7 to 3.9. The average GPA at most DO medical schools ranges from about 3.4 to 3.6.

**How many C's are acceptable for med school? ›**

In general, pre-med students are advised to retake courses in which they have earned a 'C. ' In reality, **one or two 'C's will not rule out medical school for anyone**, especially for otherwise high-achieving students.

**Is a 2.7 GPA good for medical school? ›**

"However...they don't need to have a 4.0.” While perfect grades are not required for medical school admission, premeds "would want to be in the mid-3.0 range and higher to feel relatively competitive," Grabowski says. Still, **it is possible to get into med school with a mediocre or low GPA**.

**What medical field does not require math? ›**

- Allied Health.
- Medical Assisting.
- Medical Billing & Coding.
- Occupational Therapy.
- Phlebotomy.
- Physical Therapy Assisting.
- Radiologic Technology.
- Surgical Technology.

**What job takes the most math? ›**

**14 High-Paying Jobs For People Who Love Math**

- Accountant.
- Chemist.
- Aerospace engineer.
- Mechanical engineer.
- Civil engineer.
- Marine architect.
- Economist.
- Astronomer.

**What is a job that has no math? ›**

Jobs that don't require math include **dental hygienist, security guard, and writer**. The qualifications and experience levels will vary for these types of jobs. While there are jobs that don't require math, there may be times when you may have to do math at these jobs.

**How much math is in med school? ›**

The majority of medical schools (M.D. and D.O.) with a math requirement will look for **between one and two semesters of math**. Most of them would expect a semester of calculus and a semester of statistics. No health professions schools require multivariable calculus.

### Can I become a doctor at 40? ›

There is no age limit for medical school. **You can become a doctor in your 30s, 40s, 50s, and even 60s**. In the end, medical schools want students who will make good physicians. Age is not a factor.