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lectures. Two hours credit. Professor Crittenden.

Tb. Proseminary in Roman Political Institutions. Studies in the
Imperial Period. One hour credit. Professor Sanders.
Graduate students will take this as a two-hour course, 'jd.

[7f. Tacitus, Histories. Interpretations and lectures. Two hours
credit. Professor Winter. Omitted in 1920-192 1.]

[yc.Tht Annals of Tacitus. Interpretations and lectures. Tivo hours
credit. Professor Winter. Omitted in 1920-1921.]

8. Roman Law. See Courses in Roman Law and Jurisprudence.

lOtf. TTie Topography and Monuments of Ancient Rome. Illustrated
lectures. Three hours credit. Professor Winter.
Elect as Classical Archaeology 2a,

[10^. Roman Life as Illustrated by Works of Art and Objects of
Common Use. Three hours credit. Professor Kelsey.
Elect as Classical Archaeology lb. Omitted in 1920- 192 1.]

12. Latin Writing. Advanced Course. Two hours credit,. Professors
Meader and Sanders.
In Course 12, attention is given not only to correctness of expres-
sion but also to matters of style and the finer distinctions of
the language. It is limited to those whose work in Course 11
has been of a high grade.

[16. Latin Inscriptions. Credit to be arranged. Professor Kelsey.
Reading of inscriptions of different periods from the De Criscio
collection and from reproductions. Interpretation of selected
inscriptions. Omitted in 1920- 192 1.]

i6j.The Letters of Cicero. Interpretation of selected letters, with
a study of Roman manners and political conditions at the end
of the Republic. Two hours credit. Professor Sanders.

18. Lectures on the Latin Language. Two hours credit. Professor
Meadfr.
The object of this course is to give the student a scientific basis
for the study and teaching of the Latin language. TTie sub-
jects treated will be : the history of the Latin sounds and inflec-
tions; the forms and meanings of the more important syn-
tactical types; Latin word formation.

[i8^. The Italic Dialects. Two hours credit. Professor Meader.

Lectures and recitations on the phonology, morphology, and
syntax of Oscan and Umbrian. Interpretation of inscriptions.
Omitted in 1920-1921.]



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Courses of Instruction 297

22. Teachers' Course. Virgil. Two hours credit. Professor San-
ders.
Students are required to combine 22a with 22.

[22b, Studies in Virgil. Consultation. Professor Kki.sey. No credit
given for this course. Omitted in 1920- 192 1.]

24. Reviews in Roman Literature. One hour credit. Professors
Sanders, Meader, and Winter.
Students who are candidates for advanced degrees in this depart-
ment will be given systematic reviews during the second
semester.

26. Reports on the Progress of Research. Continuation of Course
25. One hour credit,

28. Seminary. Propertius, with studies in the Roman Elegy. Pro-
fessor SAhTDERS.
Course 28 is open to graduate students only.

[31. Lectures on the Sources of Roman Historians. Professor San-
ders.
Tlie chief historians, their methods of work, their interrelation-
ships, and final indebtedness to tradition, historical records, or
their own memories, will be discussed. Incidentally, the his-
torical foundation of much in Roman history will be touched
upon. This course is intended primarily for advanced students
in Latin and teachers of ancient history. Omitted in 1920-
1921.]

SUMMER SESSION OF I92I

Zs. Caesar's Gallic War. For entrance. Professor .

4r. Virgil. Two hours credit. Professor .



7^. Latin Writing. Two hours credit. Professor Crittenden.

8j. Readings from Roman Historians. Two hours credit. Professor
Crhtenden.

2 If. Teachers' Course in Cicero. Two hours credit. Professor Crit-
tenden.

15. Latin Paleography. Two hours credit. Professor Sanders.

6a. Roman Comedy. Two hours credit. Professor ,

For Graduates and Undergraduates,

lys. The Latin Vulgate of the New Testament. Two hours credit.
Professor Sanders.



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298 Collc(jc of Literature, Science, and the Arts

27J. Tacitus. Two hours credit. Professor Sanders.

31. Direction in thesis work and in reading on historical sources and
the institutions of the Roman Empire. S'o credit. Professor
Sanders.

MATHEMATICS

(Group II)

Courses 1, 2, 3, and 4 (or equivalent courses), taken in order,
furnish the preparation preliminary to further study in any field of
pure or applied mathematics. Courses lE, 2E, 3E, and 4E are
equivalent to the courses prescribed for students in the College of
Engineering (see announcement of that College).

Courses A, C, I, lE, 2, 2E, 3, 3E, 3j, 3^, 4, 4E, 4J, 4b, 47, 48,
51, and 52 are intended primarily for undergraduates; Courses 5, 6,
7. 8, 0, II, 12, 13. 14. 19, 20, 23, 24, 25. 26, 27, 28, 29, 30, 33, 34, 49,
50, 53. 54. 55f 56, 57» and 58, are for undergraduates and graduates;
other courses are primarily for graduates, though undergraduates of
except! mal ability are admitted by special permission.

Students preparing to teach, mathematics in high schools should
take Courses i, 2 (or lE, 2E), 3, 4, 19, and ao, and five or more
hours of additional work, to be selected after conference with the
head of the department. Such conference should be had not later
than the beginning of the second year.

Students intending to specialize in Actuarial or Statistical Math-
ematics are advised to consult the instructor in charge early in their
course, and to examine carefully the program of studies under the
course in Insurance and Statistics in the special bulletin of courses
in Business Administration. Professor Glover will be in Room 405,
Mason Hall, from 10 to 12, September 20 to 24, inclusive, to consult
with students who desire to take up this work. The courses in
mathematics for students in actuarial or statistical lines of study
should be taken in the following order: I, 2, 3, (or 3E), and 51, 4
(or 4E), and 52, 13, 49 and 53, 14, 50 and 54, 55, 56.

A representative of the department of mathematics will be in
Room 108, M. 11., from 10 to 12, September 20 to 24, inclusive, to
advise students with reference to matters connected with mathe-
matical work.

first year elections

Students intending to take first-year mathematics should elect
eitlier Course A, C, I, lE, or 2, according to the following:

1. (!ourse A is intended for those who have studied neither solid
geometry nor trigonometry. A knowledge of these subjects is essen-
tial for those wishing to take up engineering mathematics.

2. Course C is for those who present for entrance to the Uni-
versity one unit (only) of algebra, and one unit (only) of geometry.



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Courses of Instruction 299

3. Coarse I is for those presenting for entrance one and one-half
units (only) of algebra, and one or one and one-half units of
geometry.

4. Course lE is for those presenting for entrance one and one-
half units of algebra, one and one-half units of geometry, and one-
half unit of trigonometry.

5. Course 2 is for those presenting for entrance one and one-
half units of geometry, two units of algebra, and one-half unit of
trigonometry.

Other students should consult a representative of the mathematics
department in regard to their elections.

FIRST SEMESTER

A. Geometry and Plane Trigonometry. Four hours credit, Mr.
Johnson.

C. Algebra and Geometry. Four hours credit. Mr. Peterson, Mr.
Anning, Mr. Field, and Mr. Halbert.

1. Algebra, Trigonometry, and Analytic Geometry. Four hours

credit. Professors Markley, Karpinski, and Bradshaw, As-
sistant Professor CoE, Mr. Johnson, Mr. Peterson, Mr. Bar-
nard, Mr. Anning, Mr. Field, and Mr. Halbert.

I E. Algebra and Analytic Geometry. Four hours credit. Professor
Ford, Mr. Johnson, Mr. Field, and Mr. Halbert.

2. Plane Analytic Geometry. Four hours credit. Assistant Pro-

fessor Cob, Mr. Peterson, and Mr. Anning.

2E. Analytic Geometry. Four hours credit. Professor Ford.

3. Calculus, I. Four hours credit. Professor Beman.

Courses 3 and 4 give considerable attention to the historical and
pedagogical aspects of the subject, and are required for Courses
19 and 20. .

3E. Calculus, I. Fitre hours credit. Professor Markley.

3a. Calculus, Shorter Course, T. Three hours credit. Professor
Bradshaw.
Courses 3<i and 4a are intended for those who, while not wishing
to specialize in mathematics, desire as a part of a lil>eral edu-
cation an acquaintance with the leading ideas of the Infini-
tesimal Calculus and its important applications.

4/^. Calculus, 11. Four hours credit. Assistant Professor Coe.



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300 College of Literature, Science, and the Arts

5. Solid Analytic Geometry. Two hours credit. Professor Beman.
Course 5 presupposes, a knowledge of the calculus. The text-
book used in Bell's Coordinate Geometry of Three Dimensions,

7. Descriptive Geometry. Three hours credit. Professor Brad-

SHAW.

A broad survey will be given of the various methods of rep-
resenting three-dimensional objects by plane figures, with pri-
mary emphasis on the geometrical theory.

9. Differential Equations. Three hours credit. Professor Beman.
Course 9 deals with the solution of ordinary and partial differ-
ential equations and is based on Johnson's Differential Equa-
tions,

II. Theory of Functions of a Complex Variable, I. Three hours
credit. Professor Markley.

See note under Course 15.

The fundamental ideas of complex numbers, their geometric
interpretation and their calculus, with introduction to the the-
ories of functions as developed by Cauchy, Riemann, and
Weierstrass.

13. Higher Algebra, I. Three hours credit. Professor Karpinski.

This course is intended to supplement the work usually done in
a short, first course in college algebra. It consists of a con-
sideration of those algebraic topics and processes commonly
used in all branches of mathematics, both pure and applied.
It should be taken by those whose interests require constant
use of mathematics, either in scientific work or in teaching.

Course 3 should precede or accompany this course.

15. Theory of Functions of a Real Variable, I. Three hours credit*
Professor Markley.
Note: — It is intended to give Courses (11, 12) and (15, 16) in
alternate years. If, however, the necessity and demand appear,
a year's work in Courses 1 1 and 15 will be given.
The purpose of Courses 15 and 16 is to investigate and obtain
a precise formulation of the necessary and sufficient conditions
for the validity of the processes of analysis, particularly the
"limiting" processes. They are concerned with such notions as
the nature of numbers, point-sets, functional relations, classifi-
cation of functions with reference to continuity, differentia-
bility, integrability, etc., with illustrative applications.

17. Theory of the Potential. Three hours credit. Professor Ziwet.



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Courses of Instruction 301

19. Teachers' Seminary. Algebra. Two hours credit. Professor
Beman.
Courses 19 and 20 are open to those who have completed Courses
I, 3 (or lE, 2E), 3, and 4.

23. Projective Geometry, II.. Three hours credit. Professor Brad-

SHAW.

Analytic projective geometry, including homogeneous coordinates
in two and three dimensions, conies, and quadric surfaces, an
introduction to the theory of invariants, and line geometry.

25. Differential Geometry, I. Two hours credit. Assistant Professor
Nelson.

27. Theory of Numbers, I. Two hours credit. Professor Karpinski.

29. Advanced Calculus, with Especial Reference to Applications in
Harmonic Analysis. Three hours credit. Professor Ford.
Adapted to those who have completed Courses 3 and 4, or the
equivalent. General topics such as the following are first con-
sidered: definite integrals, with especial reference to improper
integrals; directional derivatives; line, surface, and space in-
tegrals; Green's theorem; the derivation of Laplace's equation
•and other partial differential equations of mathematical physics

^ from elementary considerations. Applications are then made

" to problems in heat conduction, determination of potential, and

acoustics. In the early part of the course Byerly's Integral

i Calculus is used as a text, and in the latter part Byerly's

Fourier's Series and Spherical Harmonics,

31. Theory of Functions, including the Theory of Elliptic Functions.
Advanced Course, I. Two hours credit. Professor Markley.

33. Advanced Mechanics, I. Three hours credit. Professor Field.

37. Mathematical Theory of Elasticity, I. Two hours credit. Pro-
fessor ZlWET.

41. Infinite Series and Products, T. Two hours credit. Professor
Ford.

47. History of Mathematics (I). Lectures, discussions, and required
readings. Two hours credit. Professor Karpinski.
This course is especially planned to give prospective teachers of

' secondary mathematics a survey of the historical development

of the elementary branches — arithmetic, algebra, geometry,
trigonometry, and the beginnings of analytic geometry and the
calculus — ^from early times to the present. Some attention will
also be paid to an historical treatment of the methods of teach-
ing the science. A reading knowledge 9f French or German

[ is highly desirable.



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302 College of Literature, Science, and the Arts

49. Elementary Methods in Statistics. Two hours credit. Assistant
Professor Carver.
This course deals with the construction of schedules, gathering
data, editing schedules, arranging and presenting statistics in
various tabular and graphical forms.

51. Introduction to the Mathematical Theory of Interest. Three

hours credit. Professor Glover, Assistant Professor Carver,
and Mr. Barnard.

52. Introduction to the Mathematical Theory of Insurance. Three

hours credit. Assistant Professor Carver.

53. Finite Differences. Three hours credit. Professor Glover.
This course includes a study of numerous interpolation formulas,

special functions occurring in finite difference theory, finite
integration, summation of series, and solution of elementary
difference equations.
Course 53 is open to those who have completed Courses 3 (or
3E, or 3a), 4 (or 4E, or 4^), and 53.

55. Advanced Mathematical Theory of Interest and Life Contin-
gencies, I. Tour hours credit. Professor Glover.

57. Graphical Methods (I). Two hours credit. Professor Running.

59. Mathematical Theory of Statistics. Advanced Course. Two
hours credit. Mr. BARNARD.
This course will include a study of the higher characteristics of
frequency distributions and methods of graduating statistical
series as developed by Pearson and Charlier.

67. Casualty Actuarial Theory. Three hours credit. Assistant Pro-
fessor Carver.

A study of the theory and calculation of premiums and reserves
for health, accident, workmen's compensation, and other
branches of casualty insurance.

Additional courses in Mathematics will be found in the Announce-
ment of the Graduate School.

second semester

See notes at the beginning of announcement of courses in mathe-
matics in regard to first-year elections.

C. Algebra and Geometry. Four hours credit. Assistant Professor
CoE, and Mr. Johnson.

I. Algelir.i, Trigonometry. .nn<i Analytic Geomelry. Four hours
irrdif. Assistant. Professor C'oh, Mr. PETfRsoN, Mr. HxinERT.
Mr. .Awixr:, .nnd Mr. FiEi.n.



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Courses of Instruction 303

I £. Algebra and Analytic Geometry. Four hours credit. Professor
Ford.

2. Continuation of Course i. Four hours credit. Professors Mark-
ley, Karpinski, and Bradshaw, Assistant Professor CoE, Mr.
Johnson, Mr. Peterson, Mr. Barnard, Mr. Anning, Mr.
Field, and Mr. H albert.

2 £. Continuation of Course lE. Four hours credit. Professor Ford,
Mr. Johnson, Mr. Field, and Mr. Halbert.

3^. Calculus, I. Four hours credit. Assistant Professor Coe.

4. Calculus, II. Four hours credit. Professor Beman.

4£. Calculus, II. Five hours credit. Professor Markley.

4a. Calculus, Shorter Course, II. Three hours credit. Professor
Bradshaw.

6. Advanced Analytic Geometry. Three hours credit. Professor
Bradshaw.
A general survey of some of the methods of modern geometry
will be given as an introduction to synthetic and analytic
projective geometry. Some of the topics treated will be double
ratio, the involution, line coordinates, abridged notation, para-
meter equations, systems of conies, geometry of the triangle
and circle imaginary elements.

8. Projective Geometry, I. Three hours credit. Professor Brad-
shaw.
Synthetic projective geometry based largely on the works oi
Enriques and Rcye.

12. Theory of Functions of a Complex Variable, II. Three hours
credit. Professor Markley.

14. Higher Algebra, IT. Three hours credit. Professor Karpinski.
This course is a continuation of Course 13, and consists of a
more formal introduction to the subjects usually studied in a
course in the theory of equations and higher algebra.

16. Theory of Functions of a Real Variable, IT. Three hours credit.
Professor Markley.

18. Higher Plane Curves. Two hours credit. Professor Beman.
Course 18 is intended to give an introduction to the study of
algebraic curves, with special consideration of curves of the
third and fourth orders. Reference will be made to the works
of Salmon, Clebsch-Lindemann, Wieleitner, and I.oria.



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364 College of Literature, Science, and the Arts

20. Teachers' Seminary. Geometry. Two hours credit. Professor
Beman.

32. Advanced DifTerential and Integral Calculus. Three hours credit.
Professor Beman.
Course 22 is intended to give students of the calculus a reading
knowledge of some modem French work on analysis. Gour-
sat^s Cours d' Analyse, in the French or in Hedrick's transla-
tion, will be used in 1920- 192 1. Many problems from other
sources will be discussed.

24. Advanced Projective Geometry. Three hours credit. Professor
Bradshaw.
A continuation of Courses 8 and 23.

26. Differential Geometry, II. Two hours credit. Dr. Nblson.

28. Theory of Numbers, II. Two hours credit. Professor Karpin-
SKl, !

30. Advanced Calculus. Three hours credit. Professor FoRD.

A continuation of Course 29, using Byerly's Fourier's Series and
Spherical Harmonics. Consideration of Legendre Functions,
Bessel Functions, etc., and their applications in mathematical
physics.

32. Theory of Functions. Advanced Course, II. Two hours credit.
Professor Markley.

34. Advanced Mechanics, II. Three hours credit. Professor Field.

36. Vector Analysis. Three hours credit. Professor Ziwbt.

38. Mathematical Theory of Elasticity, II. Two hours credit. Pro-
fessor ZrwsT.

42. Infinite Series and Products, II. Two hours credit. Professor
Ford.

48. History of Mathematics, II. Two hours credit. Professor Kar-

PINSKI.

50. Mathematical Theory of Statistics. Introductory Course. Two

hours credit. Assistant Professor Carver.
This course deals with the elementary theory and applications
of mathematical statistics, and will include a study of such
topics as averages, measures of dispersion, and coefficients of
correlation.

51. Introduction to the Mathematical Theory of Interest. Three

hours credit. Assistant Professor Carver, and Mr. Barnard.



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Courses of Instruction 305

52. Introduction to the Mathemttical Theory of Insurance. Three
hours credit. Professor Glovkr, Assistant Professor Carver,
and Mr. Barnard.

54. Theory of Probability. Three hours credit. Professor Glover.
This course deals with fundamental concepts and seeks to estab-
lish the connection between a priori and empirical probabili-
ties. Much time is also given to the application of theorems
in selection, arrangement, distribution, and derangement to the
solution of problems in choice and chance.

56. Advanced Mathematical Theory of Interest and Life Contin-
gencies, II. Four hours credit. Professor Glovii.

60. Mathematical Theory of Statistics. Advanced Coarse. Two
hours credit, Mr. Barnard.
This is a continuation of Course 59, by which it must be preceded.

68. Seminary in Casualty Actuarial Theory. Three hours credit.
Assistant Professor Carver.

The preparation of various schedules which supplement the an-
nual statements, and a study of current articles dealing with
problems in casualty insurance, form the basis of this course.

Additional courses in mathematics will be found in the Announce-
ment of the Graduate School.

SUMMER SESSION OF I93I

80. Plane Geometry. For entrance. Assistant Professor Carver.

81. Solid Geometry. For entrance. Professor .

83. Trigonometry. Two hours credit. Professor Karhnski.

84. Algebra. Two hours credit. Assistant Professor Cos.

2. Analytic Geometry. Four hours credit. Assistant Professor CoE.

86. Teachers' Course in Geometry and Algebra. Two hours credit.
Professor Beman.

3. Calculus. Four hours credit. Professor Bradshaw.

89. Calculus. Three or five hours credit. Assistant Professors
Rouse and Hopkins.

49. Mathematical Theory of Statistics. Ttvo hours credit. Assist-
ant Professor Carver.

51. Introduction to Mathematical Theory of Interest. Two hours
credit. Professor Glover.



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3o6 College of Literature, Science, and lite Arts

52. Introduction to the Mathematical Theory of Interest and In-

surance. Two hours credit. Assistant Professor Cakvek.

63. Actuarial Exercises and Problems. Two hours credit. Assistant
Professor Carver.

96. Algebra. Two hours credit. Professor Ford.
For Graduates and Undergraduates.

48. History of Mathematics. Two hours credit. Professor Kar-

PINSKI.

53. Finite Differences. Two hours credit. Professor Glover.

54. Theory of Probability. Two hours credit. Professor Glover.
90. Differential Equations. Two hours credit. Professor Beman.
94. Advanced Geometry. Two hours credit. Professor Bradshaw.

97. Advanced Calculus. Two hours credit. Professor Ford.

MEDICAL SCIENCES

These courses may not be counted towards the hours of Literary
credit required for the Combined Curricula.

Bacteriology, Hygiene, Physiological Chemistry

The student who expects to specialize in any one of these sub-
jects should have a good training in the fundamental courses in
chemistry. The minimal requirements are Courses i and 2 in Gen-
eral Hygiene.

SECOND semester

1. General Hygiene. Three hours credit. Lectures. Professor

Vaughan.

2. General Bacteriology. Five hours credit. Lectures. Professor

NovY.

4. Advanced Bacteriology. Three hours credit. Deposit, $15. Lab-
oratory work. Professor Now.

4a. Serum Reactions and Pathogenic Protozoa. Three hours credit.
Laboratory work. Professor Now.
Courses 4 and 4a are to be elected together. They are open only
to a limited number of students, who must file their applica-
tions at least two weeks before the opening of the semester.
The deposit of $15 covers both courses.



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Courses of Instruction 307

13. Food Conservation. Three hours credit. Lectures. Assistant

Professor Emsrson.

14. Practical Study of Foods. Deposit, $5. Assistant Professor

EmersoK.
Courses 13 and 14 are to be taken together for three hours credit.

EITHER FIRST OR SECOND SEMESTER

5. Water Analysis. Three hours credit. Deposit, $io. Laboratory

work. Professor Vaughan and Mr. Chambers.

6. Food Analysis. Three hours credit. Deposit, $io. Laboratory

work. Professor Vaughan and Dr. Smith.

7. Research Work in Hygiene. Credit to be arra»iged. Professor

Vaughan.

II. Research Work in Bacteriology and Protozoology. Credit to be
arranged., Room 218. Professor Now and Assistant Profes-
sor DeKruif.

Physiology

The courses in physiology are arranged for those who intend to
become physicians and dentists; nevertheless, these courses are open
to those who have had sufficient preliminary training in physics and
chemistry, and courses in biology, particularly vertebrate anatomy
and histology. The work would be valuable to those who contem-
plate specializing in physiology, biology, or psychology.

Course i, intended especially for medical students and those who
wish to specialize in physiology, consists of lectures and recitations
dealing with general physiology, secretion, digestion, absorption, the
function o'f ductless and other similar glands, assimilation, and the
regulation of the temperature of the body. Emphasis is laid on the
physical side of these processes, as there is a course in physiological
chemistry provided for medical students.

Course 2, which is a continuation of Course i, deals with respi-
ration, circulation, and the physiology of muscle and nerve, and of
the central nervous system.

Course 3 is a laboratory course, which should be preceded by,
at least. Course 4, or some course in general physiology more advanced



Online LibraryUniversity of MichiganCatalogue of the University of Michigan → online text (page 27 of 75)