SENATE 

?

SEtThTE COMMITTEE 

.

ON UNDERGRAEXJATE S'IUDIES 

Course .... rbposal - 

th.242-3, 

Introduction to Analysis .and 

elated Calendar Changes 

18th November, 1976 

?

..

Action taken by the Senate Committee on Under- 

graduate Studies at its meeting of November 9th, 1976 gives rise 

to the following motions: 

MOTION 1 

That Senate approve, and recommend approval 

by the Board of Governors, Math.242-3, Introduction to Analysis. 

Note The Mathematics Department in one three-semester hour course 

proposes to deal in an integrated way with the material previously 

handled in two two-semester hour courses. 

MOTION 2 

That Senate approve, and recommend approval 

by the Board of Governors, a change in prerequisite such that 

Math.242-3 is made prerequisite for a 

?

course which now has? 

Math.241-2 as a prerequisite and that Math.242-3 is added as a 

prerequisite for Math.320-3, Theory of Convergence. 

MOTION 3 

That Senate approve, and recommend approval 

by the Board of Governors, a change in title for Math.141-2 from 

"Pure Mathematics I" to "Introduction to Pure Mathematics". 

Note Math 141-2 was previously entitled "Pure Mathematics I" as 

part of a sequence which also included "Pure Mathematics II and 

III". ? 

Now that the latter two courses have been fused and? 

retitled, it is appropriate to retitle the former. 

7

Daniel R. Birch 

ams

Appendix B3 

SENATE COMMITTEE ON UNDERGRADUATE STUDIES 

COURSE PROPOSAL FORM 

Calendar Information 

?

Department: Math 

p mit i s 

Abbreviation Code:MATH Course Number:242 

?

Credit Hours: _3 

?

Vector: 

Title of Course: 

Calendar Description of Course: 

Mathematical induction. Limits of real sequences and real functions. Continuity 

and its consequences. The Mean Value Theorem. The Fundamental Theorem of 

Calculus. Series 

Nature of Course ? 

Lecture/tutorial 

Prerequisites (or special instructions): MATH 152-3 or 155-3 must precede or 

be taken concurrently. Students who have obtained credit for MATH 241-2 

cannot subsequently ' 

?

MATH 242-3 

f o. ? 

What course (courses), if any, is being dropped from the calendar if this course is 

approved: 

?

MATH 142-2 and 241-2. 

2. Scheduling 

How frequently will the course be offered? 

?

Twice yearly 

Semester in which the course will first be offered? 

?

Summer 1977 

Which of your present 

'

faculty would be available to make the proposed offering 

possible: ? 

All faculty 

Objectives of the Course 

To

,

cover the important theoretical material which is at best mentioned in passing 

while teaching calculus courses, and which is important for anyone desiring to 

continue his study of analysis in mathematics. 

4.

Budgetary and Space Requirements (for information only) 

What additional resources will be required in the following areas: 

Faculty None 

Staff None 

Library None 

Audio Visual None 

Space None 

Equipment 

None 

5.

Approval 

Date: September 22. 1976 

• ? 

Department Chairman 

_____ 

Dean 

?

Chaiman, SCUS 

SCUS 73-34b:- (When completing this form, for instructions see Memorandum SCUS 73-34a. 

Attach course outline). ' 

UndergraduateCurriculumCoittee 

?

?

.From ... ... 

David Ryeburn, Chairman 

Undergraduate Studies Committee 

Faculty of                   

Mathematics Department 

Subject ...... NEW 

?

E PROP9SL:... 

MATH 2423 ? 

Date ... . .... September 2 

,

,

,               76 ................................. 

related calendar changes. 

For some time the Mathematics Department has considered the possibility of 

fusing together two existing courses, MATH 142-2 (Pure Mathematics II) and MATH 

241-2 (Pure Mathematics III). We are now ready to do so and propose a new course, 

MATH 242-3 (Introduction to Analysis). MATH 242-3 covers the important: theoretical 

material which is at best mentioned in passing while teaching calculus courses, and 

which is important for anyone desiring to continue his study of Analysisin mathematics. 

Students will find it easier to fit one 3 hour course into their sáhedules than two 

2 hour courses. We think that it will be more efficient to cover the material this 

way since material will not have to be reviewed after the semester break and thus 

very little if any of the material now covered in MATH 142-2 and 241-2 'kill need to 

be omitted. 

The prerequisite for MATH 242-3 is to be MATH 152-3 (Calculus II) br MATH 155-3 

(Calculus II for the.Biological Sciences); as an alternative students may take the 

calculus course concurrently. MATH 242-3 is to be a prerequisite for every course 

now having MATH 241-2 as a prerequisite. Moreover ., we wish to include MATH 242-3 

as an additional prerequisite for MATH 320-3 (Theory of Convergence) which currently 

has MATH 253-4 as its only prerequisite. Our experience in offering that course 

for the past year shows that most of those students who have not taken MATH 241-2 

have much more difficulty with MATH 320-3 than those who have already taken MATH 241-2. 

The final calendar change necessitated by the introduction of MATH 242-3 is the 

change in title for MATH 141-2 (now called Pure Mathematics I). This course was 

considered to be part of the 141-2, 142-2, 241-2 sequence. We would like to request, 

as a result of the replacement of 142-2 and 241-2 by 242-3, that the title for 

141-2 now be "Introduction to Pure Mathematics". 

David Rye rn 

Undergraduate Curriculum Committees, 

Faculty of Arts 

Faculty of Education 

Faculty of Interdisciplinary Studies 

.

Syllabus 

?

1.:. 

.

?

MATH 242-3 

Introduction to Analysis 

1.

Brief survey of some ideas from Logic - connectives, quantifiers, 

proofs, sets and functions. 

2.

Mathematical induction. 

3.

Sequences and series of real numbers. 

4.

Limits, continuity, and differentiability for real functions 

5.

Continuous functions and their properties - the Intermediate, 

Value Theorem, Maximum-Minimum properties, uniform continuity. 

6.

Theorems of Calculus - Mean Value Theorems, Fundamental Theorem 

of Calculus, Introduction to the idea of uniform convergence. 

TEXT: The Theoretical Side of Calculus, by Cohn Clark 