Linear algebra is a useful tool with many applications within the computer science field. This paper will cover the various applications of linear algebra in computer science including: internet search, graphics, speech recognition,and artificial intelligence. A major focus of linear algebra in computer science is internet searches, which involves finding techniques for effectively storing and searching through information. In the year 2000 there was an estimated 2.5 billion web pages on the internet
Eigenvalues and eigenvectors is one of the important topics in linear algebra. The purpose of this assignment is to study the application of eigenvalues and eigenvectors in our daily life. They are widely applicable in physical sciences and hence play a prominent role in the study of ordinary differential equations. Therefore, this assignment will provide explanations on how eigenvalues and eigenvectors will be functional in a prey-predator system. This will include background, history of the concept
well as they can earn profit at the same time, businesses will need to consider the impact to the prices of product that effected by society. In Linear Algebra in the Financial World, Barbara Swart (2001) uses the example of determine the price of the gold and the price changing in different period of time to tells about the relationship between Linear Algebra and the Financial World. Between 1999 and 2000, there is a Y2K bug with the computers and many other electronic items because of the early setting
place in which something is formed or produced. The history of matrices goes back to ancient times! But the term "matrix" was not applied to the concept until 1850. The origins of mathematical matrices lie with the study of systems of simultaneous linear equations. The term "matrix" for such arrangements was introduced in 1850 by James Joseph
hyperplanes are defined using kernel functions. The most popular kernel types are supported: linear, polynomial, radial basis and sigmoid. Support Vector Machines can be used for both, classification and regression. Several characteristics have been observed in vector space based methods for text classification [15,16], including the high dimensionality of the input space, sparsity of document vectors, linear separability in most text classification problems, and the belief that few features are relevant
2004) Principal components seek to transform the original variables to a new set of variables that are (1) linear combinations of the variables in the data set, (2) Uncorrelated with each other and (3) ordered according to the amount of variation of the original variables that they explain (Everitt and Hothorn 2011). The Assumptions of PCA: Linearity- The reduced dimension should represent the linear combination of the original variables. The importance of mean and covariance- There is no guarantee that
Table of Contents Numerical Integration 2 Trapezoidal Rule 2 Simpson’s Rule 3 Roots of Equation: 4 Fixed‐Point Iteration 4 Newton‐Raphson Method 4 Systems of Linear Equations 4 LU Decomposition 4 Gauss‐Seidel 4 References: 4 Numerical Integration Numerical integration consist of a wide variety of different method for calculating the area under the curve. Some of the ones that I will cover in this portfolio are the Trapezoidal Rule and the Simpson 1/3 Rule. I will explain how some
application, computer animation, etc.) Matrices was discovered and developed in the 18th and 19th century, the development of matrices had to do with the transformation of geometry and solutions of linear equations. Historically the early emphasis was not on the matrix but on the determinant. Now when performing algebra, matrix is heavily considered as a factor. Matrix has its important factor in mathematics however physicists and biologists also have their fair use of matrices in terms of organizing and studying
Part 1: 1. Algebra is a branch of mathematics that deals with properties of operations and the structures these operations are defined on. Algebra uses letters and symbols to represent numbers, points, and other objects, as well as the relationships between them. It is an important life skill that emerges as a prerequisite for all higher-level mathematical education as well economic program. There are 5 reasons for studying algebra. Firstly, algebra can help us in our career. As we know, the
Unlike geometry, algebra was not developed in Europe. Algebra was actually discovered (or developed) in the Arab countries along side geometry. Many mathematicians worked and developed the system of math to be known as the algebra of today. European countries did not obtain information on algebra until relatively later years of the 12th century. After algebra was discovered in Europe, mathematicians put the information to use in very remarkable ways. Also, algebraic and geometric ways of thinking
the largest fields of study in the world today. With the roots of the math tree beginning in simple mathematics such as, one digit plus one digit, and one digit minus one digit, the tree of mathematics comes together in the more complex field of algebra to form the true base of calculations as the trunk. As we get higher, branches begin to form creating more specialized forms of numerical comprehension and schools of mathematical thought. Some examples of these are the applications into chemistry
fractional. The Egyptians used the fraction 2/3 used with sums of unit fractions (1/n) to express all other fractions. Using this system, they were able to solve all problems of arithmetic that involved fractions, as well as some elementary problems in algebra (Berggren). The science of mathematics was further advanced in Egypt in the fourth millennium BC than it was anywhere else in the world at this time. The Egyptian calendar was introduced about 4241 BC. Their year consisted of 12 months of 30 days
fractions, squares, cubes and roots. The evidence of using Pythagorean triples was also traced as part of Hindu mathematics long before Pythagoras. The Indian text known as “Sulba Sutras” contains a geometric approach in finding the solutions of linear and quadratic equations. The use of circle to represent zero is usually attributed to Hindu mathematics. Early Indians are also known to be the first to establish the basic mathematical rules for dealing with zero. They had also established the laws
going to be an accountant. The drive to learn more and share what I learned exposed me. After fulfilling the algebra requirement, I realized that I enjoyed algebra. So I took more math classes, just for the fun of it. I stayed up late, working additional problems, caught up in the thrill of understanding. I became an unofficial tutor, helping my classmates with factoring and linear equations. It was fun helping them learn. Whipping around the room from one student to the next was exhilarating
S. Gudder once wisely stated, “The essence of mathematics is not to make simple things complicated, but to make complicated things simple.” Many people have different views of mathematics and the role it plays in their life. There are some students who believe that learning mathematics is useless and is not a necessity for their major, and there are others who find math, arithmetic, and numbers easier to process. I find Gudder’s thoughts to be true based on my upbringings and recent experience
more high powered mathematical development. Number problems such as that of the Pythagorean triples (a,b,c) with a2+b2 = c2 were studied from at least 1700 BC. Systems of linear equations were studied in the context of solving number problems. Quadratic equations were also studied and these examples led to a type of numerical algebra. Geometric problems relating to similar figures, area and volume were also studied and values obtained for p.The Babylonian basis of mathematics was inherited by the Greeks
of Gö ttingen. In 1799, he obtained his doctorate in absentia from the University of Helmstedt, for providing the first reasonably complete proof of what is now called the fundamental theorem of algebra. He stated that: Any polynomial with real coefficients can be factored into the product of real linear and/or real quadratic factors. At the age of 24, he published Disquisitiones arithmeticae, in which he formulated systematic and widely influential concepts and methods of number theory -- dealing
Rae Steinheiser Grubisic Honors Algebra I Period 6 1 May 2014 Writing Assignment: Math of the Ancient Egyptians Introduction The Ancient Egyptians are commonly known as the first people to use geometry. Not only did they use it, but they were masters of it. Their work constructing the pyramids only provides evidence of their vast mathematical knowledge. The Ancient Egyptians invented many different mathematical techniques in order to make daily life easier. Luckily, there are still records from the
Number Grids Investigation Introduction In the following piece of coursework, I intend to investigate taking a square of numbers from a 10 x 10 grid, multiplying the opposite corners and then finding the difference between the two products. I was first asked to take a 2 x 2 square from a 10 x 10 grid, multiply the opposite corners and then find the difference. This is the result I received; 2x2 squares 15 16 25 26 Square 1 15 x 26 = 390 16 x 25 = 400 Difference
It’s hard to believe that a civilization consisting of once illiterate nomadic warriors could have a profound impact on the field of mathematics. Yet, many scholars credit the Arabs with preserving much of ancient wisdom. After conquering much of Eastern Europe and Northern Africa the Islamic based Abbasid Empire transitioned away from military conquest into intellectual enlightenment. Florian Cajori speaks of this transition in A History of Mathematics. He states, “Astounding as was the grand march