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Siatc Conmii.ttcc onGraduate Studies 

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Dean of Science

Sed

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:heinati cs Gra dnat:e çq)c 

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Do' ,  

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October22 1969      

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C

1

an go s 

At its 

meeting of October 20th the Faculty of Sd once approved 

the

deletion of Math. 

805-4 

and the addition of Math 80--4 in 

the graduate program. These changes had previ.us1y received the 

approval of the Faculty of Science Graduate Studi.cs 

Conmdtt:ce

I would apprec.ste it if you wouj.d ensure 

that these changes are 

considered by the Senate Graduate Studies Co;aaitt:ec at the earli cst 

opportunity so t:hal: the material may be bought to Senate in ti 

for . 

inclusion ill the 1970-71 Ca] cedar. 

c.

?

Dr. A. ii. Lach 

l

an

Acting head 

•

Mathematics 

Mi. s s M. MeG 

Approved by the Executive Committee of the Senate Coimijittee on 

Graduate Studies, November 1969. 

(

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(:?

j? ScU•C 

3. ii) Report of the Graduate Studies Committee 

b) Deletion of Math 805-4 and Addition of Math 808--4 

The Mathematics 808-4 Course was approved by the Faculty of 

Science Graduate Studios Committee at its meeting of September 17, 1959 

It is recommended that the Faculty approve this course and that 

it be submitted to Senate for approval 

B. L. Punt 

Approved by the Faculty of Science at its meeting of October 20

)

1969

:.i'cj

Toy Graduate Studies Committee From

A. H. Lachlan, Cha:L:cia

cu:Lty of Sc:i.en.ce ?

Graduate Studies Coiitte

Matheina.t Ic s J)po.:i:bren.t

Date: September 12,

1969

Ile should like

approval

for the deletion Of

Math 80H Logic I

from the calendar and for thc addition of

Math OoG

) ?

Logic i:i:: ,

By this means we hope to improve the quality of our graduate

offerings in Hathematical Logic. Since 1967 our two basic

graduate courses in logic have been Math

LOgIC

i: flflU

Math 80

Log:c ii. It should be noted that 805 uas never

a prerequisite f or

806.

The course 805 treated recurs:.ve

function theory and 

had little connection with 806, ibich

is concerned 

vith 

the theory of formal systems. 

For the proposed new course 808, 806 will be a

prerequisite ?

Some recursive function theory \Ti.11. be taugii;

in 808, and its relevance to the material in 806 will be 

made clear. 

Ytir

important topics not px'cviously taught 

in 80

JOG \/:LL.L be Inc ludeci in 808.

Iii conclusion, this change is proposed bocause

the faculty members in Logic: (Gerber, Harrop

Ltchlan,

Thomason) agree that the combination of 806, 808 viil:i.

(:OTlStitt\tO

a more satisfactory grounding in mathematical

Logic than the, combination.

UO, 806.

-I

)Propo::; ed Nc Graduate Course. in athcnaLi.cs

L. Cal ender Information

liathematics

80E4

Logic III

Prerequisite: Mathematics 806'

Students who have obtained credit for Mathematics

8054

may not obtain credit for

Mathematics 80

2. Course Iescr.pti.c)n

(fit present

this iru.:L

not appear in the calendar

since no course descriptions appear for Mathematics graduate 

courses. ) 

Introduction to recursion theory, ('ch' 

s Thesis

Goc1el'Boseer incompleteness theorem, undecidability, 

kiCenC

normal form theorem, the en::cation theorem, the recurs ion 

theorem. The arithmetical hierarchy, the analytical hierarchy. 

Degrees of un;olvah.ity. }Tcisis theoreiuie

I\dditional topici

if time

Text: Chapters 

6,7,8

of Mathematica)

• : ? 

J. B. Shoenfiold, Addison Wesley 

J.967.

(The earlier part 

Of this book is covered in iiat.hc-ruiatics 

8O64. )

Enrollment and Schedulinr 

The course will be offered when student demand 

warrants it and Departmental resources permit. It is proposed, 

to offer it for the 

first 

time in 70'1 if the necessary 

pproval can he obtained

in time. 

. Justification 

(i)

BLL2Lc

This course, to be substituted for i.'iathematics

8054

Logic I, will enhance our basic offerings in matheruiati' 

cE). logic . at the graduate level, (See the covering memoran- 

dum), The department has attracted a steady stream of gradu° 

ate

students whose main interest is logic. 

3.

(ii)

i,Lc!icic.

Mathemat.cs ? 

LiC I 

V ?

(iii)Course Overlap 

There 

is substantia:L overlap 

with Mathematics 

which is to be 

discontinued, 

but

neg3.igtbJ.c 

OVorla)) with 

other 

courses offered 

in the University. 

1 /^ 

L

,J/ , - ^^, V.", 

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