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Mathematics

2. Mathematics is not just an indispensable tool for science and business. It is a rich and beautiful field worthy
of study for its own sake. A mathematics major will learn to think logically, gain an aesthetic appreciation
for the subject and develop the skills to solve quantitative problems.
Graduates of our program include teachers, professors, lawyers, actuaries, business managers, computer
scientists, architects, and financial advisors. Mathematics is a respected major that prepares students to
enter any field where quantitative ability is valued.
Our mathematics program allows majors enough room in their schedules to either take a minor or possibly
a second major in another subject. In recent years we have seen mathematics majors with second majors
in biology, computer science, finance, music, economics, Spanish, psychology, and other subjects. The
second major or minor is chosen based on an interest of the student, or with a particular career in mind.
Students who are planning to teach mathematics at the high school level enroll as mathematics/secondary
education majors.These students take all the coursework of the mathematics majors, and additional
courses from the education department. They also student-teach in a high school during their senior year.
Majors who are intending to enroll in a Ph.D. program in mathematics often take extra mathematics
courses beyond what is required. A true hallmark of the program is the willingness of faculty to engage in
independent study or research with students who want to study more advanced topics in preparation for
graduate school. In recent years our majors have earned a Ph.D. at universities that include Notre Dame,
Brown, Tufts, U.C. Santa Barbra, University of Massachusetts, and SUNY Stony Brook.
The College usually graduates between 20 and 30 mathematics majors each year. By the sophomore year,
the classes for the major usually have between 15 to 20 students, and often less.
Computer Science
The computer science program at Providence College graduates students who have practiced solving
problems--using the tools of algorithms to create solutions and using high-level programming languages to
implement these solutions.
They have the knowledge of networks, databases, operating and numerical methods of solving problems,

3. and the mathematics that underlies the field of computer science. They have the opportunity to develop
mobile apps and to create internet programs. But the most important thing they have learned is to apply
their problem-solving skills in new areas and using new languages.
Some Computer Science graduates have excelled in computer science graduate programs. Others have
excelled in industries where they have used proprietary language as well as the languages they learned at
Providence College. They often return to the College to speak to current students and they often volunteer
to assist current students in their job search.
Greetings from the Chair
Jeff HoagWelcome to the web pages of the mathematics and computer science department. Here you can
find information about our courses and programs. You can also learn about department activities and the
achievements of our students, alumni, and faculty.
Please feel free to contact me or any other member of the department if you would like more information.
Lynette J. Boos, Chair
Mathematics and Computer Science Department lboos@providence.edu
Clare Boothe Scholarships
PC recently received its first major grant award from the Clare Boothe Luce Program at the Henry Luce
Foundation. The award will support eight Clare Boothe Luce Undergraduate Scholarships in chemistry, appl
ied physics, mathematics, or computer science for exceptional senior female students.
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4. Mathematics and Computer Science
Howley Hall 218
Phone: 401.865.2334
Fax: 401.865.1356
Lynette J. Boos, Ph.D.
Chair
lboos@providence.edu
Lynne DeMasi
Administrative Assistant
ldemasi@providence.edu
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Providence, RI 02918 USA
Tel: +1.401.865.1000
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Relativistic Doppler Shift
The normal Doppler shift for waves such as sound which move with velocities v much less than c is given by
the expression
where the plus sign is taken for waves traveling away from the observer. For light and other
electromagnetic waves, the relationship must be modified to be consistent with the Lorentz transformation
and the expression becomes
Here v is the relative velocity of source and observer and v is considered positive when the source is
approaching.
Derivation Calculation Low velocity limit (v/c small)‎
Index
Doppler concepts
HyperPhysics***** Relativity R Nave
Go Back

11. Doppler Effect, Electromagnetic Waves
The Doppler effect is observed with visible light and all other electromagnetic waves. Just as in
the case of sound waves, the wavelength in the direction of the source motion is shortened to
where all quantities here are measured in the observer's frame. To relate this to the source frequency, it
must be expressed in terms of by using the time dilation expression
This is used to get the frequency.
Relativistic Doppler effect Calculation
Index
Doppler concepts
HyperPhysics***** Relativity R Nave
Go Back
Fractional Wavelength Change
For purposes of determining recession speed of stars and galaxies with the Doppler effect by observation of
the red shift of spectral lines, it is convenient to express the Doppler effect in terms of the shift in
wavelength compared to the source wavelength. For these purposes it is more convenient to define a
receding velocity as positive in the wavelength relationship:
The fractional wavelength change is defined as the z parameter for characterizing red shifts:

12. In terms of the usual relativity symbols, this becomes
Derivation Calculation
Index
Doppler concepts
HyperPhysics***** Relativity R Nave
Go Back
Doppler Frequency
From the Doppler shifted wavelength, the observed frequency is
Rearranging gives the convenient form
where the relative velocity vs is positive if the source is approaching and negative if receding. In terms of
the usual relativity symbols, this becomes
Relativistic Doppler effect Calculation Comparison with sound Low speed approximation
Index
Doppler concepts
HyperPhysics***** Relativity R Nave

13. Go Back[]NEGERISETTI2000[]
Relativistic Doppler Shift
The normal Doppler shift for waves such as sound which move with velocities v much less than c is given by
the expression
where the plus sign is taken for waves traveling away from the observer. For light and other
electromagnetic waves, the relationship must be modified to be consistent with the Lorentz transformation
and the expression becomes
Here v is the relative velocity of source and observer and v is considered positive when the source is
approaching.
Derivation Calculation Low velocity limit (v/c small)
Index
Doppler concepts
HyperPhysics***** Relativity R Nave
Go Back
Doppler Effect, Electromagnetic Waves
The Doppler effect is observed with visible light and all other electromagnetic waves. Just as in
the case of sound waves, the wavelength in the direction of the source motion is shortened to
where all quantities here are measured in the observer's frame. To relate this to the source frequency, it
must be expressed in terms of by using the time dilation expression

14. This is used to get the frequency.
Relativistic Doppler effect Calculation
Index
Doppler concepts
HyperPhysics***** Relativity R Nave
Go Back
Fractional Wavelength Change
For purposes of determining recession speed of stars and galaxies with the Doppler effect by observation of
the red shift of spectral lines, it is convenient to express the Doppler effect in terms of the shift in
wavelength compared to the source wavelength. For these purposes it is more convenient to define a
receding velocity as positive in the wavelength relationship:
The fractional wavelength change is defined as the z parameter for characterizing red shifts:
In terms of the usual relativity symbols, this becomes
Derivation Calculation
Index
Doppler concepts
HyperPhysics***** Relativity R Nave
Go Back

15. Doppler Frequency
From the Doppler shifted wavelength, the observed frequency is
Rearranging gives the convenient form
where the relative velocity vs is positive if the source is approaching and negative if receding. In terms of
the usual relativity symbols, this becomes
Relativistic Doppler effect Calculation Comparison with sound Low speed approximation
Index
Doppler concepts
HyperPhysics***** Relativity R Nave
Go Back