Algorithm design is the branch of discrete mathematics and computer science that deals with the research, development and implementation of sequential and asynchronous algorithms. While there aren’t really any jobs with the title algorithm designer, most graduate-level computer science work involves quite a bit of algorithm theory and research. Algorithms are used in every field that deals with values that can be quantified and many fields that deal with values that cannot. An algorithm is simply a sequence of instructions; a recipe is an algorithm, and so is a list of driving instructions.

### The Importance of Algorithms in Computer Science

The reason algorithms are used so often in computer science is that computers can be programmed to execute each instruction in a sequence, allowing programmers to instruct computers how to render 3-D graphics, display text and perform various operations on numbers. The first uses of computers were to perform basic arithmetic operations on huge volumes of numbers, sometimes requiring several months to return an answer that would take a few seconds or minutes on today’s hardware. Computer scientists at the time didn’t realize that algorithms could be used to program computers to make photo-editing and design applications, video games and automated financial trading software.

These sophisticated programs that are often used to process unquantifiable data are constructed from hundreds or thousands of short functions that are themselves constructed of hundreds or thousands of processor instructions. The smallest unit of a computer program is an instruction, which is a simple operation performed on the bits contained in a processor register. The operations that can be performed on the bits of data depend on the processor architecture, and they typically involve switching certain bits from zero to one, shifting bits to the left or right and other similar, simple transformations of base-two, or binary, numbers. For example, to multiply a base-two number by two, all of the bits in a register are shifted to the left, similar to the way every digit in a base-10 number is shifted to the left when it’s multiplied by 10: 15 becomes 150, 150 becomes 1500, and so on.

### How People Benefit From Algorithms

High-level programming languages like C, C++, Java and Python allow programmers to write extremely complicated programs with relatively little code. For example, a C++ program that executes a linear search algorithm can check every element in an array with just two or three lines of code, but the same sequence of instructions written in Assembly language might require 20 or 30 lines of code.

The most common algorithms in programming are sorting and searching functions, and there are always efforts being made to make them more efficient. One of the most important concepts in computer science is the question of P versus NP, or whether the set of polynomial-time algorithms is the same as the set of nondeterministic polynomial-time algorithms, according to the Clay Mathematics Institute. If they’re the same, then computer scientists could solve problems that would take millions of years to solve using currently known algorithms. Most people think P and NP are not equal.

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When only one instruction can be executed at a time, an algorithm must be performed sequentially, but quantum computing could make today’s technology obsolete, according to Scientific American. If you have a graduate-level interest in discrete mathematics and computer science, consider going into algorithm design.