History of Mathematics, an Introduction
Fall Semester 2019
1 Instructor
Prof. Richard Carey
Office: POT 965
E-Mail richard.carey@uky.edu
Phone: (859) 257-3745
Office Hours: MW 2-3 and by appt.
From The Bulletin of Course Descriptions:
A survey of the development of mathematics. Topics may include: the Egyptians and Babylonians,
mathematics of the Greek Classical Age, Euclid and the Alexandrian School,the Renaissance,
Fermat and the beginning of calculus, the work of Newton and Leibnitz, nineteenth
century geometry, analysis and set theory. Prequisite MA 114.
More specific research topics from your textbook and the web include:
From Geometry: Theory of area; famous construction problems; history of the parallel
postulate and non-euclidean geometry; Bolyai-Lobachevsky formula for the angle of parallelism
and distance:
tan α/2 = e^{−d/k}
where k is the constant whose square occurs in the proportionality factor for area to defect.
From Number Theory: The fundamental theorem of arithmetic; Fermat’s Christmas theorem;
Fermat’s Little theorem; Fermat’s Last theorem; Bernoulli formula for the sum of k-th
powers; prime number theorem, clock arithmetic and the Law of Quadratic-Reciprocity; p-adic
numbers; Diophantine equations, cryptology .
From Algebra: Complex numbers and the fundamental theorem of algebra, cubic and quartic
equations, solutions of equations of degree five or greater; algebra of quaternions; algebraic
number theory, algebra of matrices and vectors, axiomatic algebra - groups, rings and fields;
mathematics of the search engine.
From Calculus: Origins of calculus. Fundamenal Theorem of calculus as exemplified by
the theorems of Green, Stokes and Gauss; Maxwel’s electromagnetic equations, calculus of
variations and the principle of least action; infinite series which leads to celebrated formulas
such as
e^{iπ} +1 = 0, and sum{ n=1 to infinity} 1(/n^2) =(π^2)/6.
.
From Probability: Statistical probability and gambling on Wall Street and casinos on the
boat or in Las Vegas and Macau, set theory and counting, The law of large numbers, the central
limit theorem.
2 Text:The text for the course is The History Of Mathematics, An Introduction; 7th edition.by
David M. Burton. This text is online at
MacTutor History of mathematics archive. For fun check out the top 100 theorems list.
3 Grading Your course score will be the sum of two take-home exam assignments (100),
and a take-home final exam (130) The grading scale for the course will be as follows:
297-330 A; 264-296 B; 231-263 C; 198-230 D; < 198 E.
The Final Exam is due no later than 5 pm on Wednesday December 18.
4 Attendance: Grading for the course will be influenced by class attendance. You will be
allowed 4 unexcused absences, then for every missed class after that you will lose 10 points
from the possible 330. I will let you know later when roll begins.
5 Additional Course Policies: Course policy of academic accommodations due to disability:
If you have a documented disability that requires academic accommodations, please see
me as soon as possible during scheduled office hours. In order to receive accommodations
in this course, you must provide me with a Letter of Accommodation from the Disability
Resource Center Course policy for attendance: See the above. Make-up opportunities: The
instructor shall give the student an opportunity to make up the work and/or the exam missed
during an excused absence... implies the student shall not be penalized for the excused absence.
Verification of Absences: Students missing work due to an excused absence bear the
responsibility of informing the instructor about their excused absence within one week following
the period of the excused absence (except where prior notification is required) and
of making up the missed work. Course policy for submission of assignments: Students shall
return all assignments on the due date. No late assignments shall be accepted without an
excused absence. Course policy on academic integrity: All assignments, projects, and exercises
completed by students for this class should be the product of the personal efforts of the individual(
s) whose name(s) appear on the corresponding assignment. Misrepresenting others work
as ones own in the form of cheating or plagiarism is unethical and will lead to those penalties
outlined in the University Senate Rules (6.3.1 and 6.3.2) at the following website: http :
//www.uky.edu/USC/New/rulesregulations/index.htm. The Ombud site also has information
on plagiarism found at http : //www.uky.edu/Ombud.Course policy on classroom civility and
decorum: The university, college and department has a commitment to respect the dignity of
all and to value differences among members of our academic community. There exists the role
of discussion and debate in academic discovery and the right of all to respectfully disagree from
time to time. Students clearly have the right to take reasoned exception and to voice opinions
contrary to those offered by the instructor and/or other students (S.R. 6.1.2). Equally, a faculty
member has the right - and the respon- sibility - to ensure that all academic discourse occurs in
a context characterized by respect and civility. Obviously, the accepted level of civility would
not include attacks of a personal nature or statements denigrating another on the basis of race,
sex, religion, sexual orientation, age, national/regional origin or other such irrelevant factors.
Please note Senate Rule 6.4.7.A.1 has changed. The Registrar will retain a record of the Letter
of Warning for an academic offense. It will be available to third parties if the student authorizes
its release or the specific record is requested as part of a court-ordered subpoena. In the past,
the Registrar destroyed the record of the offense when the student graduated.
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