**MTH 381/URI** **History
of Mathematics**

**Course
Information and Syllabus, Spring 2020**

**Text**:

* History
of Mathematics*, David M. Burton, Sixth
Edition

Supporting literature:

S. Krantz, *An
Episodic History of Mathematics*
(free download)

printed version can be purchased:

*An
Episodic History of Mathematics: Mathematical Culture through Problem
Solving (Maa Textbook)*

Prerequisites: MTH 141 or 131

**Exams and Grading**:
There will be two exams, some homework assignments, and the final
presentation.

The exams and quizzes are of open book type. Cell phones, ipads, ipods, etc. should beturned o during the quizzes and exams. Excepted from this are electronic pads and laptops used for notetaking. In particular laptops with electronic version of the book are allowed.

Calculators are permitted in this class.

PRESENTATIONS, QUIZZES, AND HOMEWORK: 40 percent

FINAL PRESENTATION: 20 percent

**Aims and Objectives-Short Version**

The course aims to illustrate the following:

**1**.
How mathematics has been, and still is, a developing subject.

**2**.
How advances in mathematics are driven by problem solving and how
initial formulations often lacked rigor.

**3**.
How good mathematical notation is vital to the development of the
subject.

**4**.
How mathematical ideas that are considered "elementary"
today have great level of sophistication.

**5**.
To teach you how to use the library and technology, especially the
internet.

**6**.
To improve your oral and written communication skills in a technical
setting.

By the end of the course students are expected to be able to:

**1**.
understand, describe, compare and contrast the main ideas and methods
studied in the course.

**2**.
apply the methods to given examples.

**3**.
develop a broad historical appreciation of the development of
mathematics.

**4**.
understand that even very abstract results of pure mathematics affect
everyday lives.

**5**. have
effective presentation style in a technical setting.

**Objectives-Detailed Version**

The main aim of this course is to introduce the study of the history of mathematics. This means both telling the story of the development of mathematics in the past, and practicing the historical judgments and methods that enable the story to be told. The course should also deepen your understanding of the role the mathematics has played in society.

**Topics**

The course is intended for interested people from a variety of backgrounds: students of mathematics who want more understanding of its historical development, teachers of mathematics at all levels, who will find such material enriching to their students' learning, and people who have a general interest in social and cultural history.

Our approach is based on texts and the materials that can be found on the Internet.

The major topics that will be covered are:

* Mathematics
in the ancient world*
moves from the earliest evidence for mathematical activity,
before the time of the Egyptians and Babylonians, through the
achievements of classical Greece to Euclid's

**Through
the Middle Ages to the seventeenth century****.**
We follow the development of the algebraic approach through Muslim
culture and then the rediscovery in Europe of classical Greek texts
at the end of the sixteenth century, which helped lead to a flowering
of mathematics in the next century. We look at the time of Napier
(logarithms) in Scotland; Descartes (algebraic geometry) in France;
Kepler in Germany and Galileo in Italy applying mathematics to the
world; and the invention of the calculus.

* The
seventeenth and eighteenth centuries.* The
calculus was invented, independently and in rather different ways, by
Newton and Leibniz (building on the work of many earlier
mathematicians). What were the consequences of this? We trace some
developments through the eighteenth century, and examine how
algebraic concerns reached almost their modern form in the work of
the great Swiss mathematician Leonhard Euler.

* Topics
in nineteenth-century mathematics.* Is Euclid's
'parallel postulate' necessarily true, or can other logically
consistent geometries be devised? Can a formula be found for solving
equations of the fifth degree or, if not, why not? Were the
foundations of the calculus secure - if not, what to do about it?
Can calculation be mechanized, and at what cost? Can you 'prove' a
theorem by using a computer? These are some of the questions
discussed in this survey of characteristic topics of
nineteenth-century mathematics that are the basis for many of the
concerns and approaches of mathematics in the twentieth century.

**Topics
in twentieth century mathematics***.
*This part is based on the students project which brings a
brilliant collection of 20th-century mathematical theories, leading
the reader on a fascinating journey of discovery and insight.

**Special Needs**

Section 504 of the Rehabilitation act of 1973 and the Americans with Disabilities Act of 1990

require the University of Rhode Island to provide academic adjustments or the accommodations

for students with documented disabilities. The student with a disability shall be responsible for

self-identication to the Disability Services for Students in the Oce of Student Life, provid-

ing appropriate documentation of disability, requesting accommodation in a timely manner, and

follow-through regarding accommodations requested. It is the students responsibility to make ar-

rangements for any special needs and the instructors responsibility to accommodate them with

the assistance of the Oce of Disability Services for Students. Any student with a documented

disability is welcome to contact me as early in the semester as possible so that we may arrange

reasonable accommodations. As part of this process, please be in touch with Disability Services for

Students Oce at 330 Memorial Union, 401-874-2098, http://www.uri.edu/disability/dss/.

Important links:

and **History
of Difference Equations and Recursive Relations**

We
will use the following link for the variety of topics and biographies
oh mathematicians:

The
MacTutor History of Mathematics archive

**Instructor**: Dr. M. Kulenovic, Lippitt 202 D,
X44436,

e-mail: **mkulenovic@mail.uri.edu**

**Online information**:
*www.math.uri.edu/courses *or
*www.math.uri.edu/~kulenm* **Office
hours**: MW: 9-10:30,

**Time**: MWF:
12-12:50
**Room: Engineering Building 264**