Mathematics has had an incredible impact on technology as we know it today. Understanding this impact aids in understanding the history of how technology has developed so thoroughly and what significant events happened to facilitate such an advanced society. A better understanding can be derived by analyzing the historical background on the mathematicians, the time periods, and the contributions that affected their society and modern society as well as specific examples of how the mathematical developments affected society. Math had and has a great impact in technology. During the 20th century mathematics made very quick advances on all fronts. Mathematics sped up the development of symbolic logic as the foundation of Math became solidly grounded. Aside from logic, physics and philosophy also benefited from the quantum theory and the relativity theory during this time. New fields were developed like the chaos theory, the game theory and computational mathematics. During the 20th century, mathematics reached broader application than any other time before.

David Hilbert (1862-1943) was born in East Prussia. He studied and taught at the University of Konigsberg, East Prussia until the mid 1890's. He soon transferred to the University of Gottingen which he later developed into a very popular mathematical center.

Hilbert was a mathematician of many fields like calculus of variations and the number theory. However he made a significant contribution in the field of geometry. His contribution to integral equations influenced the study in functional analysis.

Alfred North Whitehead - (1861-1947) Born in Ramsgate, England Whitehead was a professor of Mathematics at the University of Cambridge and Trinity College, University of London and Harvard University He made great contributions in the theoretical mathematics

Hermann Minkowski - (1864-1909) He was born in Russia, he moved to Germany where he...

...Mathematical logic is something that has been around for a very long time. Centuries Ago Greek and other logicians tried to make sense out of mathematical proofs. As time went on other people tried to do the same thing but using only symbols and variables. But I will get into detail about that a little later. There is also something called set theory, which is related with this. In mathematical logic a lot of terms are used such as axiom and proofs. A lot of things in math can be proven, but there are still some things that will probably always remain theories or ideas.
Mathematical Logic is something that has a very long history behind it. It has been debated on for many centuries. If someone were to divide mathematical logic into groups they would get two major groups. Both groups are very long. One is called "The history of formal deduction" and it goes all the way back to Aristotle and Euclid and other people who lived at that time. The other is "the history of mathematical analysis" which goes back to the times of Archimedes, who was in the same era as Aristotle and Euclid. These to groups or streams were separate for a long time until Newton invented Calculus, which brought Math and logic together.
Somebody who studies mathematical logic and gives his or her own concepts about it is called a logician. Some well known logicians include Boole and Frege. They were...

...FRENCH CONNECTION SEQUENCE ANALYSIS
For this sequence analysis, I have chosen a scene from William Friedkin’s The French Connection. The scene chosen is the chase sequence and confrontation between Popeye Doyle and the sniper on the roof who worked for “Frog number one”. I believe that this sequence differs from classical Hollywood conventions in a numbers of important ways, marking it quite clearly as a different sort of film to the police procedurals which may have come before it.
The sequence begins with Popeye Doyle walking back to his apartment, whereupon a sniper kills a young mother with a bullet intended for Doyle. Despite this being an innocent woman caught in the cross-fire, Doyle shows little concern overall and we do not later learn her fate, unlike a classic Hollywood film where some sadness or remorse would be shown by Doyle over the death of this innocent person. This foreshadows his later complete disregard for killing of the FBI agent at the conclusion of the film, showing Doyle to perhaps be without the morals, honor and integrity we would normally assume of our Hollywood cop “heroes”.
Doyle chases the sniper, losing him at a train station and commandeering a car to follow the train to its next stop. The chase is shown from inside the car, angles behind and in front of the car and in wide-angle shots. Interspersed with this, we see the sniper heading to the front of the train, shooting guards and hijacking the driver....

...LECTURE NOTES ON MATHEMATICAL INDUCTION
PETE L. CLARK
Contents
1. Introduction
2. The (Pedagogically) First Induction Proof
3. The (Historically) First(?) Induction Proof
4. Closed Form Identities
5. More on Power Sums
6. Inequalities
7. Extending binary properties to n-ary properties
8. Miscellany
9. The Principle of Strong/Complete Induction
10. Solving Homogeneous Linear Recurrences
11. The Well-Ordering Principle
12. Upward-Downward Induction
13. The Fundamental Theorem of Arithmetic
13.1. Euclid’s Lemma and the Fundamental Theorem of Arithmetic
13.2. Rogers’ Inductive Proof of Euclid’s Lemma
13.3. The Lindemann-Zermelo Inductive Proof of FTA
References
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1. Introduction
Principle of Mathematical Induction for sets
Let S be a subset of the positive integers. Suppose that:
(i) 1 ∈ S, and
(ii) ∀ n ∈ Z+ , n ∈ S =⇒ n + 1 ∈ S.
Then S = Z+ .
The intuitive justiﬁcation is as follows: by (i), we know that 1 ∈ S. Now apply (ii) with n = 1: since 1 ∈ S, we deduce 1 + 1 = 2 ∈ S. Now apply (ii) with
n = 2: since 2 ∈ S, we deduce 2 + 1 = 3 ∈ S. Now apply (ii) with n = 3: since
3 ∈ S, we deduce 3 + 1 = 4 ∈ S. And so forth.
This is not a proof. (No good proof uses “and so forth” to gloss over a key point!)
But the idea is as follows: we can keep iterating the above argument as many times
as we want, deducing at each stage that since S contains the natural...

...Mathematical modeling is commonly used to predict the
behavior of phenomena in the environment. Basically,
it involves analyzing a set of points from given data
by plotting them, finding a line of "best fit" through
these points, and then using the resulting graph to
evaluate any given point. Models are useful in
hypothesizing the future behavior of populations,
investments, businesses, and many other things that
are characterized by fluctuations. Amathematical
model usually describes a system by a set of variables
and equations which form the basis of the
relationships between the variables.
The variables represent independent and dependent
properties of the system. Models are classified in a
variety of ways. One of these ways is "linear versus
nonlinear." A linear model is any system whose
behavior can be explained or predicted using a linear
equation or an entire set of linear equations. On the
other hand, a nonlinear model uses at least one
nonlinear equation to describe its behavior. Models
may also be classed as either deterministic or
probabilistic. A deterministic model always performs
the same way under a given set of initially occurring
conditions, while a probabilistic model is
characterized by randomness. Another way of evaluating
models is to determine whether it is static or
dynamic. Static models do not account for time, while
dynamic models do take this element into
consideration. In calculus,...

...Mathematical modelling of a hyperboloid container
Mathematical model is a method of simulating real-life situations with mathematical equations to forecast their future behaviour. Eykhoff (1974) defined a mathematical model as 'a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form'. Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social sciences (such as economics, sociology and political science); physicists, engineers, computer scientists, and economists use mathematical models most extensively.
Mathematical modelling uses tools such as decision-theory, queuing theory, and linear programming, and requires large amounts of number crunching. Mathematical modelling approaches can be categorized into four broad approaches: Empirical models, simulation models, deterministic models, and stochastic models. The first three models can very much be integrated in teaching high school mathematics. The last will need a little stretching. Empirical modelling involves examining data related to the problem with a view of formulating or constructing a mathematical relationship between the variables in the problem using the available data. However,...

...Mathematics Modeling
Introduction
Mathematics finds its root way back more than 5000 years. Mathematics has helped people solve complex problems, represent different problems and transfer knowledge and skill about the different problems. Mathematical models have often being developed to solve and represent these problems especially in natural sciences and engineering disciplines (Arnold 2000). Mathematical models can be defined as a mathematical language that would describe the behavior of a system or rather a problem. Mathematical modeling can be done to develop scientific understanding, test a system for change and help in making decision (Anon 2005).
Urban Population change
The urban population change represents one of the most important aspects that define a city. The household composition and their nature differentiate the urban population from that in the area. Urban population is growing much faster than the population as a whole. It is prospected that, in the next century, more than half the population will be living in the urban centers. The changes of the population have shaped the cities to function as social, economic and cultural centers. The urban population growth has been witnessed more in the developing countries especially in Africa and Asia continents. The large change in urban population can be attributed to the industrial revolution. Rural to urban migration has remained the main cause of...

...ABSTRACT
MATEL, PABLO B., Reading Comprehension and Mathematical Problem-Solving Skills of Fourth Year High School Students of Tagaytay City Science National High School, SY 2013 – 2014. Master’s Thesis. Master of Arts in Education major in Mathematics Cavite State University, Indang, Cavite. Octber 2013. Adviser: Dr. Constancia G. Cueno.
This study determined the relation between reading comprehension skills and mathematical problem-solving skills of fourth year high school students of Tagaytay City Science National High School. Specifically, the study aimed to: describe the profile of the students in terms of age, gender, birth order, parents’ educational attainment, parents’ occupation, and monthly family income; determine the level of reading comprehension skills of the students; determine the level of mathematical problem-solving skills of the students; determine the significant differences in the students’ reading comprehension skills when grouped according to age, gender, birth order, parents’ educational attainment, parents’ occupation, and monthly family income; determine the significant differences in the students’ mathematical problem-solving skills when grouped according to age, gender, birth order, parents’ educational attainment, parents’ occupation, and monthly family income; and determine the significant relationship between students’ reading comprehension skills and...

...9. 1.
9.2.
9.3.
9. The soft interview
Introduction
Soft questions and answers
Finance data questions
297
297
297
303
C+十
223
223
226
233
Chapter 10. Top ten questions
10. 1. Introduction
10.2. Questions
305
305
305
Bibliography
307
309
Preface
What this book is and is not
Please support the author! If you find this book
The purpose of this book is to get you through your first interviews for quant
beneficial, purchase a hard copy!
jobs. We have gathered a large number of questions that have actually been asked
and provided solutions for them all. Our target reader will have already studied
and learnt a book on introductory financial mathematics such as "The Concepts
and Practice of Mathematical Finance." He will also have learnt how to code in
C++ and coded up a few derivatives pricing models , and read a book such as
"C++ Design Patterns and Derivatives Pricing."
This book is not intended to teach the basic concepts from scratch, instead it
shows how these are tested in an interview situation. However, actually tackling
and knowing the answers to all the problems will undoubtedly teach the reader a
great deal and improve their performance at interviews.
Many readers may find many of the questions silly and/or annoying , so did
the authors! Unfortunately, you have to answer what you are asked and thinking
the question is silly does not help. Arguing with the interviewer about why they
asked you...