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Sample Topics

### Discrete Math

Discrete Math Discrete mathematics is a category of mathematics that deals with the objects discretely or rather distinctly. Unlike the term ‘continuous’ used in real analysis, the values in discrete are treated separately. The study of Discrete mathematics involves the concepts like sets, relations and functions, graph theory, Boolean algebra, probability, counting theory etc. The main applications of Discrete mathematics are in the computer science field for computing, programming languages, algorithms, cryptography, etc.
Sample Questions: ### Finite mathematics

Finite mathematics is the part of calculus. It is concerned with limits, finite number of variables, linear programming, elementary matrix algebra, introduction to probability, mathematics of finance etc. Finite mathematics gives a survey of mathematical techniques and has many applications in day to day life, such as linear programming is used for transportation optimization, Probability is used in weather prediction, sports strategies etc.
Sample Questions: ### Applied Mathematics

Applied Mathematics is concerned with mainly focused on the applications of Mathematics. It deals with the applications of calculus, differential equations. etc. Important applications of applied part are in the field of business, life sciences, social science, computer science, etc.
Sample Questions: ### Mathematical biology

Biology is a category of mathematics that deals with the study and theoretical analysis of living organisms. The mathematical problems that require the knowledge of biology comes under this division of mathematics. Main topics that come under this are Mainly related to real life problems that relates to cell biology, ecology, evolution, molecular biology, etc. One of the most common and well-known problem it deals with is Cancer-Inspired Free Boundary Problem.
Sample Questions:

1. A drug is given at an infusion rate of 50 mg/h. The drug concentration value determined at 3.2 h after the start of the infusion is 8 mg/L. Assuming the patient has 5.4 L of blood, estimate the half-life of this drug. Round your answer to two decimal places.

2. In a sorority with 40 members, 18 take Mathematics, 5 take both Mathematics and biology, and 8 take neither Mathematics nor Biology. How many take Biology but not Mathematics.

3. What is the difference between discrete and distributed time delay in mathematical biology? advantage and disadvantage?

4. (a) Why Is Mathematical Biology So Hard?

(b) What is one example of a biological question to solve using mathematics?

Business mathematics is the arithmetic used by profitable firms to evident and accomplish corporate maneuvers.  Commercial organizations make use of mathematics in financial analysis, forecasting, inventory management, accounting and marketing. Business management can be done more efficiently by making use of more advanced mathematics like linear programming, calculus and matrix algebra.
Sample Questions:

1. What did you learn in business mathematics class especially related to payroll?

2. John invested \$15,000 in a mutual fund for 4 years ago. If the fund grew at the rate of 9.8%/year compounded monthly, what would John’s account be worth today?

3. Determine the utilization and the efficiency for each of these situations: A. A loan processing operation that processes an average of 7 loans per day. The operation has a design capacity of 10 loans per day and an effective capacity of 8 loans per day. B. A furnace repair team that services an average of four furnaces a day if the design capacity is six furnaces a day and the effective capacity is five furnaces a day. C. Would you say that systems that have higher efficiency ratios than other systems will always have higher utilization ratios than those other systems? Explain.

4. WDH Incorporation has borrowed \$1,000,000 to purchase new factory equipment and the company must repay the loan in 5 years, quarterly at 7% interest rate and interest rate per period is 1.75%. Find the quarterly payment to be made by the company to discharge the loan in time.

### Operation Research

OR is signifies research on operations. OR is a scientific method of providing explicit quantitative understanding and assessment of complex situations for better decision making. In operation research, problems are broken down into basic components solved by constructing mathematical models and deriving the solution of the model. Operation research used for solving different types of problems like problem dealing with the waiting line, problem dealing with the allocation of materials etc. Operation research has a several types of methods like linear programming, network flow programming, integer programming, non-linear programming, and dynamic programming.
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