I am a medical doctor, with a post-graduate specialisation in Pathology, specifically, Clinical Microbiology. Maybe I can shed a little light, although my advice will be slanted toward the Singapore medical system, so your mileage may vary.
Depending on the surgical subspecialty, you may be using a little math in your day to day stuff. Orthopaedics surgeons often deal with angles of deformity, and need to do accurate goniometric measurements of ranges of motion, etc. in their follow-up of patients. Neurosurgeons need to have a fair understanding of hydrostatics principles in managing conditions like hydrocephalus, and in measuring cerebrospinal fluid pressures and managing shunts that have been put in place to relieve intracranial pressure. Stereotactic brain surgery needs even more precision, but the math is probably all going to be done by computers. As an obstetrician, you'll have to be quick with simple mental arithmetic to calculate the gestational age, expected due date, gravity and parity status, etc, but there are simple hand held calendrical calculators to do all this stuff.
Surgeons are of course, medical doctors, and as a doctor, you'll need to use math to titrate dosages, react to abnormal values appropriately (e.g. calculate the right dose of insulin to administer to a patient in a particular state of hyperglycemia). You'll also need to use simple math (including square roots) in interpreting electrocardiograms (ECGs, or EKGs as they're known in the US). There are formulae used to estimate Creatinine Clearance (a measure of excretory kidney function) using the serum creatinine, weight, body surface area, age, sex, etc. and a relation known as the Cockcroft-Gault equation. So you see, lots of simple math in workaday medical stuff, but nothing that really stresses you beyond high-school level stuff.
If you do certain other specialisations, more math/physics may be required. For example, if you specialise in Radiation Oncology, you may need to calculate very precise doses of radiation so as to treat, but not overtreat, your patients. If you do epidemiology, you may need LOTS of math to do mathematical modelling, including ordinary and partial differential equations and various stochastic methods. But this is really a fringe discipline, strictlykfor the mathematically-inclined.
In medical school, here's a breakdown of the math that may be required:
Biochemistry: basic organic chem involves some fiddling around with dissociation and acid-base-buffer equilibria. You may need to solve quadratic equations to resolve some problems. Enzyme kinetics involve simple mathematical models like Michaelis-Menten kinetics and Hill kinetics. You'll need to understand the solution of first order ordinary differential equations to derive those equations which yield you Km and Vmax values, and the principle of first-order kinetics. You'll need to design and carry out experiments that involve careful titration of micromolar concentrations. You may need to use a UV spectrophotometer (we did).
Physiology: understanding ionic equilibria involves a good working grasp of the Nernst equation and the Goldman-Hodgkin-Katz equilibrium. You'll need to really "get" all this when you try to describe how an action potential is generated, and its sequelae. Some other stuff like visual physics, and auditory physics - including understanding the decibel scale, sound intensity i. W/m^2, etc.
Pharmacology: apart from titrating doses by body weight/surface area, you'll need to understand drug kinetics very well. This involves concepts like first-pass metabolism and the area-under-the-curve, which is defined as \int_0^{\infty} C(t)dt, where C(t) is the concentration of drug at time t. Half-life, steady-state (at approx. 5 half-lives), drug peak and trough concentrations are all concepts you need to be familiar with.
Community medicine, epidemiology: lots of math here. You'll need to cover basic statistics, covering both parametric (t-test, etc.) and non-parametric (Spearman rho, etc.) tests. You may need to do systematic reviews that involve meta-analysis, using fixed or random-effects models and the appropriate statistics.
I hope I've painted a reasonably complete picture of the sort of math you may encounter in Medicine. Good luck!
