which these letters come will be studied, and †17. Paul's Epistles to the Corinthians. The period M. Second Term, Summer Quarter, 1896–7. *17. The Epistle to the Romans. Introduction, full †20. The Miracles and the Parables of Christ. A collection and classification of the Gospel miracles, a study of Christ's purpose, principles, and methods in their use, and a consideration his torically of the miraculous element in the Gos- 21. The Teaching of Jesus. A study of the record of Christ's teachings with reference to the principles to be applied in arranging and understanding the same, a classification of the material under specific topics and a thorough discussion of the main themes of Jesus' teaching, including its relation to the religious thought of his time. DM. Autumn Quarter, and *Summer Quarter. MR. VOTAW. Courses B20 and 21 are intended especially for students in the University Colleges and Graduate School. All other courses are open to students in the English Theological Seminary and in the Academic Colleges. XVII. THE DEPARTMENT OF MATHEMATICS. OFFICERS OF INSTRUCTION. ELIAKIM HASTINGS MOORE, PH.D., Professor of Mathematics. OSKAR BOLZA, PH.D., Professor of Mathematics. HEINRICH MASCHKE, PH.D., Assistant Professor of Mathematics and Physics. WILLIAM HOOVER, PH.D., Non-Resident University Extension Assistant Professor of Mathematics. J. W. A. YOUNG, PH.D., Instructor in Mathematics. JAMES HARRINGTON BOYD, Sc.D., Tutor in Mathematics. HARRIS HANCOCK, PH,D., Assistant in Mathematics. H. E. SLAUGHT, A.M., Reader in Mathematics. J. I. HUTCHINSON, A.B., Docent in Mathematics. INTRODUCTORY. The courses of instruction offered by the Mathematical Department will be considered under the heads: ELEMENTARY MATHEMATICS, Introduction to the Higher MathematicS, MODERN MATHEMATICS. ELEMENTARY MATHEMATICS. The course, Required Mathematics (two consecutive Double Minors), includes in order the following subjects: Plane trigonometry, the elements of the analytic geometry of the conic sections, and the elementary theory of finite and infinite algebraic and trigonometric series. This course is, as a means of general culture, required of every academic college student in the first year of residence. This course will be given in 1894-5 in seven sections; course 1, sections 1a, 1b, 1c, 1d, during the Autumn and the Winter Quarters; course 2, sections 2a, 2b, 2c, during the Winter and the Spring Quarters. Students wishing to study Physics or Chemistry or to elect Culture Calculus should enter section 1a, 1b, 1c, or 1d. Course 4, Analytics and Calculus (three consecutive Double Minors, Autumn, Winter, and Spring Quarters), should be taken as the Academic College Elective by students intending to make a special study of Mathematics, Astronomy, or Physics. Course 5, Culture Calculus (Double Minor, Spring Quarter), is elective for those students who do not intend to make a special study of Mathematics, and yet are desirous of having at least a glimpse of what lies beyond the elements of the subject. These courses are given at least once a year. INTRODUCTION TO THE HIGHER MATHEMATICS. The courses on the theory of equations, advanced integral calculus, advanced analytic geometry, differential equations, the applications of calculus to geometry, analytical mechanics, the elements of projective geometry, the elements of elliptic functions, and the elements of the theory of functions. These courses are intended primarily for students of the University College making Mathematics their principal subject, and for those making Mathematics their secondary subject, in particular for students of Astronomy, and of Physics. Especial care will be taken to secure a practical familiarity with the application of calculus to the solution of analytical, geometrical, and mechanical problems. The student is advised to elect the courses on the theory of equations and advanced integral calculus as early in his course as possible; they are necessary for almost all further work. Candidates for the master's degree with Mathematics as principal subject are expected to cover satisfactorily the topics above mentioned or their equivalent. The more important courses are given annually. MODERN MATHEMATICS. The instruction offered in the Graduate School is intended to give the student a comprehensive view of modern Mathematics, to develop him to scientific maturity, and to enable him to follow, without further guidance, the scientific movement of the day, and, if possible, to take an active part in it by original research. To this end general courses on the most important branches of modern Mathematics, such as: Theory of functions of a complex variable, elliptic functions, theory of invariants, modern analytical geometry, higher plane curves, theory of substitutions, theory of numbers, synthetic geometry, quaternions, theory of the potential, are given at least once in two years, while other courses of a more special character and the Seminars are intended to introduce to research work. THE SUMMER QUARTER. The courses of the Summer Quarter are designed to meet the needs of college men and others wishing to study advanced Mathematics who are able to spend only the summer in residence. The courses and Seminars of a series of four summer quarters will be arranged so as to give a wide view of modern Mathematics.* The attention of any student wishing the guidance of the department in his continuation of the work done in the summer is called to the correspondence courses of the department given under the auspices of the University Extension division of the University. (See page 111 of this Register.) FACILITIES. The Department is provided with the more important mathematical periodicals, collected works, treatises and text-books, as well as with a selection of Brill's models. Three fellowships are reserved for Graduate Students of Mathematics. * Preliminary announcements for the Summer Quarter of 1895 are made on page 111 of this Register. COURSES OF INSTRUCTION. 1894-5. 1. Required Mathematics. Plane trigonometry, the elements of the analytic geometry of the conic sections, and the elementary theory of finite and infinite algebraic and trigonometric series. [NOTE.-Any student permitted to matriculate with entrance conditions in Mathematics is expected to remove these conditions at the next regular entrance examination, and, until this has been done, he may not take the required college mathematics.] 2 DM. Autumn and Winter Quarters. Section la, Section 1b, Section 1c, DR. BOYD. DR. BOYD. DR. HANCOCK. Section 1d, DR. HANCOCK. Prerequisite: Entrance Algebra and Plane and Solid Geometry. 2. Required Mathematics. The same as Course 1. 2 DM. Winter and Spring Quarters. Section 2a, MR. SMITH and DR. HANCOCK. Section 26, MR. DICKSON and DR. HANCOCK. Section 2c, MR. BROWN and DR. BOYD. 3. Plane Trigonometry. The analytical chapters of the subject will receive especial emphasis. M. First Term, Summer Quarter. 4. Analytics and Calculus. This course (five hours weekly through the Autumn, Winter, and Spring Quarters) should be taken as Academic College elective in their second year of residence by those students intending to make a special study of Mathematics, the course Required Mathematics having been taken in their first year of residence. Autumn Quarter. Presupposing the sketch of analytic geometry contained in the Required Mathematics, and based on Casey's Treatise on Conic Sections (Longmans, Green & Co., New York; edition of 1893), a detailed study of the conic sections, in which also the newer methods of analytic geometry (abridged notation, homogeneous point- and line-coördinates) will come into play. Winter and Spring Quarters. Based on Greenhill's Differential and Integral Calculus (Macmillan, New York; second edition, 1891), an elaborate study of the differential and of the elements of the integral calculus, with numerous applications to problems of geometry and of mechanics; the elements of analytic geometry of three dimensions. Aside from but in connection with the regular work of this course the instructor will hold a Colloquium: two-hour sessions fortnightly. Members of the Colloquium will be assigned special problems and subjects to investigate. (Students admitted after personal interview with the instructor.) 3 DM. Autumn, Winter, and Spring Quarters. DR. BOYD. Prerequisite: The course Required Mathe matics. 5. Culture Calculus. Introduction to the Differential and Integral Calculus. This course is planned to illustrate the principles, methods, and applications of the calculus, and its relations to modern mathematics. It is general and summary rather than detailed and exhaustive, and is intended to give to those who do not wish to study Mathematics further an idea of this the most important, characteristic, and indispensable instrument of mathematical thought. A text-book is used largely supplemented by lectures. This course is not sufficient basis for a further study of Mathematics or its applications. Those wishing to specialize in Mathematics, Physics, or Astronomy should elect Course 4, Analytics and Calculus. DM. Spring Quarter. DR. YOUNG. Prerequisite: The course Required Mathe matics. 6. Plane Analytic Geometry. This course (five hours weekly during the Summer Quarter) is intended for students having a thorough knowledge of algebra and plane trigonometry, and a fair knowledge of the elements of analytic geometry. Casey's Treatise on Conic Sections (Longmans, Green & Co., New York; edition of 1893). DM. Summer Quarter. MR. SMITH. 6A. Differential and Integral Calculus. For those beginning the subject. M. First Term, Summer Quarter. 7. Differential and Integral Calculus. This course is intended for students having a good knowledge of plane analytic geometry and of the elements of the calculus. Byerly's Differential Calculus 8. Determinants. Burnside and Panton's Theory of Equations (Longmans, Green & Co., New York; third edition, 1892) will be the basis of the course. M. First Term, Summer Quarter. 9. The Theory of Equations. Burnside and Panton's Theory of Equations is used as the basis of the work, being supplemented by lectures by the instructor and by reports by the students on topics for reading not treated in the text. Chapters I-XIV of the text are taken up. The more important supplementary topics considered are: Continued fractions, with applications to quadratic irrationals; applications of determinants (Jacobians; m linear equations in n variables, mn; linear transformation of linear forms in n variables; orthogonal substitutions; reduction of quadratic forms in ʼn variables to a sum of squares); various proofs of the "fundamental theorem of algebra"; linear and binomial congruences. 2 DM. Winter and Spring Quarters. DR. YOUNG. Prerequisite: Analytic Geometry and the Dif ferential Calculus. 10. Advanced Integral Calculus. Including definite integrals, Fourier's series, and the elements of elliptic integrals and functions. 2 DM. Autumn and Winter Quarters. ASSISTANT PROFESSOR MASCHKE. Prerequisite: Differential Calculus and the elements of Integral Calculus. 11. Differential Equations. This course is a continuation of Course 10, Advanced Integral Calculus, and is devoted primarily to the technique of differential equations; that is, to the solution of such equations by known functions, by series, and by definite integrals. Based on chapters I-IX of Forsyth's Differential Equations (Macmillan, New York; second edition, 1888). The more important applications and methods of the broader theory of differential equations will be sketched. Aside from but in connection with the regular work of this course the instructor will hold a Colloquium: two-hour sessions fortnightly. Members of the Colloquium will be assigned special problems and subjects to investigate. (Students admitted after personal interview with the instructor.) DM. Spring Quarter. DR. BOYD. 12. Analytic Geometry of Three Dimensions. The geometry of planes and quadric surfaces. DM. Winter Quarter. PROFESSOR Bolza. Prerequisite: Analytics and Calculus. 13. Analytic Mechanics. The elements of statics and dynamics. Application to practical problems. The fundamental principles of mechanics and the elements of the theory of the potential. DM. Spring Quarter. ASSISTANT PROFESSOR MASCHKE. Prerequisite: Analytic Geometry and a thorough knowledge of Differential and Integral Calculus. 14. Projective Geometry. Reye's Geometrie der Lage (Baumgärtner, Leipzig; third edition, 1892) will be used as the basis of the course. DM. Autumn Quarter. PROFESSOR MOORE. 15. Invariants with Applications to Higher Plane Curves. This course is intended primarily for those who can be in residence only during the Summer Quarter. The aim is to give a general introduction to the subject, outlining its scope, bearings, and literature, and to prepare the student to do later more detailed reading privately. The introduction is given by means of lectures by the instructor and reports by the students on assigned readings. DM. Summer Quarter. DR. YOUNG. Prerequisite: Differential Calculus, Determinants, and the Theory of Equations (as given for instance in Byerly's Differential Calculus and Burnside and Panton's Theory of Equations). 16. Higher Plane Curves. Geometric aspect of the theory of invariants of binary quantics. Homogeneous point- and line-coördinates. General theory of higher plane curves in connection with the theory of invariants of ternary quantics. Special study of curves of the third and of the fourth order. DM. Autumn Quarter. ASSISTANT PROFESSOR MASCHKE, Prerequisite: Analytic Geometry and elements 23. Theory of Functions of a Complex Variable. The of Theory of Invariants. 17. Algebraic Surfaces. Homogeneous coördinates in space. Extension of the general theory and 18. Configurations. The elements of projective geometry of space of n dimensions. The more important general classes of configurations; certain special configurations, in particular those connected with the number six. The course will be conducted by the lecture-seminar method. DM. Spring Quarter. PROFESSOR MOORE. Prerequisite: Courses 12, 14, and 16. 19. Theory of Numbers. This course treats of the divisibility of numbers, congruences, quadratic residues, and quadratic forms. No specific subjects are prerequisite to this course, but those electing it should have had mathematical training at least equivalent to that required for Course 15. DM. Summer Quarter. DR. YOUNG. 20. Theory of Numbers. The same as Course 19. DM. Winter Quarter. DR. YOUNG. 21. Introduction to the Theory of Quaternions. The elements of the theory with applications to geometry and mechanics. DM. Autumn Quarter. PROFESSOR BOLZA. Prerequisite: A thorough knowledge of Analytics and Calculus. 22. Theory of Functions of a Complex Variable. The theories of Cauchy and of Weierstrass Based on Forsyth's Theory of Functions (Macmillan, New York; 1893). DM. Summer Quarter. PROFESSOR MOORE. Prerequisite: A thorough knowledge of Diferential and Integral Calculus and of the Theory of Equations (as given, for instance, in Byerly's Differential Calculus and Integral Calculus, and in Burnside and Panton's Theory of Equations). theories of Cauchy and of Weierstrass. DM. Autumn Quarter. PROFESSOR BOLZA. Prerequisite: A thorough knowledge of Differential and Integral Calculus and of the Theory of Equations. 23A. Calculus of Variations. Based on the developments of Weierstrass and Schwarz. DM. Winter Quarter. DR. HANCOCK. Elliptic Functions. Schwarz's "Formelsammlung" will be the basis of the course. A number of examples will illustrate the application of Weierstrass's methods to problems of geometry and mechanics. 24. Weierstrass's Theory of DM. Winter Quarter. ASSISTANT PROFESSOR MASCHKE. Prerequisite: Elements of Theory of Functions. 25. Theory of Substitutions. The general theory of substitution-groups and its applications to algebraic equations. DM. Winter Quarter. PROFESSOR BOLZA. Prerequisite: Theory of Equations. 26. Elliptic Functions. The fundamental properties of elliptic functions as deduced from the theta functions; the principal algebraic equations of the theory. The course will be based on the first two parts of Weber's Elliptische Functionen und algebraische Zahlen (Vieweg, Braunschweig; 1891). DM. Summer Quarter. PROFESSOR MOORE. Prerequisite Elements of the Theory of Functions and of the Theory of Substitutions. 27. Functions Seminar. Memoirs and problems relating to the theory of functions are assigned to the members of the Seminar for reading and investigation. Two- to three-hour sessions of the Seminar are held fortnightly. Anyone conversant with the theory of functions or in attendance upon either Course 22 or Course 26 may become a member of the Seminar. |