course material

1. MATH111 Introductory Linear Algebra
Answers:
Mathematics is a crucial part, especially in modern life; without it, life has no much meaning.
From the olden days, mathematics existed and has undergone a series of changes in the
methods and approaches used to calculate them. Before the arrival of modern-day
electronic calculators, people would spend time doing calculations by hand, which was
considered a profession. Mechanical calculators, as well as logarithm techniques, were often
engaged for use in banks, by astronomers, and other scientists. Without history,
contemporary people will tend not to appreciate technology and assume that things like
electronic calculators were there and are normal life gadgets.
The process of mathematics discovery can be regarded as an evolution of ideas, from the
use of primitive logarithms, which were tedious and involved many steps, to the modern-
day use of electronic and digital calculators. The use of logarithms was first coined by John
Napier between 1550 and 1617. The first copy of his book, which was published in Latin,
came to light in 1614 and was followed by other books he wrote on many subjects such as
mathematics and religion. John Napier also invented a device used for performing long
multiplications named "Napier's Bones." Coming to the 17th century, Johannes Kepler,
another scientist, appreciated the work of Napier by using his logarithms in his calculations,
which led to the development of the laws of planetary motion. His calculations would have
taken several years, but Napier's logarithms helped him shorten his calculation, and he had
to congratulate and acknowledge this work through a letter. Kepler's laws of planetary
motion formed the basis of evidence supporting the theory of universal gravitation as put
forward by Sir Isaac Newton. The transition and inter-dependence of ideas from one scholar
to the other and acknowledgment of others' work as useful in their discoveries grants us the
freedom to say that the mathematical discovery process is not a stop shot goal but an
evolution of ideas.
Modern mathematics has better shaped the way we think, approach, and perceive our daily
calculations. Electronic calculators found a way of shortening long, complex mathematics
steps into simple short integrated calculations. This can be a reason why researchers claim
that the current generation tends to be much different from the old generation in terms of
the level of reasoning, complexity, and creativity. Nevertheless, technology is appreciated

2. and welcomed as a life-changing aspect. Modern computing has doubled the life of every
mathematician by making life hustle free in calculation and doing away with iterative long-
step calculations. However, in recent decades scientists such as Laplace would attest that
mathematics evolution doubles life where he quoted logarithms shortening labor 200 years
after its discovery.
Currently, most fields, if not all, require mathematics knowledge to effectively undertake
daily routine activities. Although professionals study mathematics for entry into their
chosen career, its application cannot be limited to studied discipline. There are a vast array
of applications from across all fields that apply mathematics skills, especially in the
contemporary dynamic life fast with technology. Some contents or ideas in mathematics
published papers that seemed useless sometimes back are finding their application in the
current world, implying that even the basic and abstract mathematics such as logic and
number theory is very useful. Hardy's mathematics on number theory was 50 years ago
regarded as the least useful but is currently a vital prerequisite to various applications such
as financial records protection, remote satellite data transmission, and automated system
control.
Bibliography
Aspray, William, and Philip Kitcher, eds. History and philosophy of modern mathematics.
Vol. 11. U of Minnesota Press, 2018.
Beckenbach, Edwin F., and Royal Weller. Modern Mathematics for the Engineer: First Series.
Courier Corporation, 2013.
Kramer, Edna Ernestine. The nature and growth of modern mathematics. Princeton
university press, 2012.
Rice, Brian, Enrique A. González-Velasco, and Alexander Corrigan. The life and works of
John Napier. Springer, 2017.
Wilder, Raymond L. Evolution of mathematical concepts: An elementary study. Courier
Corporation, 2013.