Math 112, Numbers: From 2*0 = 0 to e^{2pi i} = 1

Table of contents :
Full set of notes in pdf [291 pages: i-vi + 1-285]
Title and Contents.pdf [6 pages: i-vi]
Introduction.pdf [4 pages: 1-4]
Chapter 1.pdf Notation, Undefined Concepts, Examples [14 pages: 5-18]
Chapter 2.pdf Fields [36 pages: 19-54]
Chapter 3.pdf Induction and Integers [28 pages: 55-82]
Chapter 4.pdf Complexification of a Field [9 pages 83-91]
Chapter 5.pdf Real Numbers [14 pages: 92-105]
Chapter 6.pdf Complex Numbers [19 pages: 106-124]
Chapter 7.pdf Complex Sequences [34 pages: 125-158]
Chapter 8.pdf Continuity [17 pages: 159-175]
Chapter 9.pdf Properties of Continuous Functions [6 pages: 176-181]
Chapter 10.pdf The Derivative [20 pages: 182-201]
Chapter 11.pdf Infinite Series [24 pages: 202-225]
Chapter 12.pdf Power Series [35 pages: 226-260]
Bibliography.pdf [6 pages: 261-265]
Appendix A.pdf Operations on Z/n [3 pages: 266-269]
Appendix B.pdf Hints and Answers [5 pages: 269-273]
Appendix C.pdf List of Symbols [4 pages: 274-277]
Index.pdf [8 pages: 278-285]

Citation preview




     

           !#"$ %'&)(+*-,/.10 243 06587:9=/=/?






  
   !"$#"%  % 
+*  2 !  



% & # -.



& #&@.  A 0 #5 'E F - 

%  %

aD ;

% 



4

$B7

 

# 



2

376 ; 0/G& #

*13$F7"/G& 

 % 'e" _h F hg g i^ NM G eS jO P

 3#

P)PP)PP)P)PPP)PP)PP)P)PP)PP)PPP)P)PP)PP)P)PP)PPP

P Z

3 %

PU

'e" F G ]K G G K JDS  L'e"   9i=D+8B - ( ba S  F Sg NM G K S6O  9i!=D+8B   ! (  'e" 9 %" &   " LR" & )8B P

.i- ! 

P Z

]

PU

aO

P

aO/ # 


 

 #

 E  4  &H #C# & - 3 4 

 

]

' i- $C  F 

ZeP Z

XD

ZeP U

 #

7

 #

ZeP _

H
4   I % &



ZeP W

3

Z^Z

P)P)PP)PP)PPP)P)PP)PP)P)PP)PPP

%   C 

 4  $ .

PP)PP)PP)P)PP)PP)PPP)P)PP)PP)P)PP)PPP

.

&& C  C  B7



ZeP Y

ZeP

]

TT

P)PP)PP)P)PP)PP)PPP)P)PP)PP)P)PP)PPP

 E  4  &

ZeP

ZeP

P)PPP)PP)PP)P)PP)PP)PPP)P)PP)PP)P)PP)PPP

F


 )    




h

J*J O  . #   #  b

F.
 3 . # 



\E 

Z


#L 3P

:. " I Xb)

#3 &)_

C #3$3 E $ A7 

%  %  #3!C 

- E&5

Z^

_

U F . X . U . " I X

# 

/





U F 87*PL %! 

$





 3& .&

/G



# 

/

7

$

-B %

#  C# P

& c

 C 3  #





F#Y

P





 



& # & C 



 

# 


 


 

Z^

$



P

/G

.

c M

3 % 3 # 

# 

7d
 % 3 %

 #$3  # PH.&

& A 3  
 4 

&

/



 


#



& 

h

78,


^







$#

.& C! c78' !C 

,PF 3



.

$#

 C$ 

78

U X



ZeP Y

V

7  # 


#

.& C! B78

i- #5O#5 



& I& O$#





F

 .

 

$#

F. FV



$#

#  7



& C! c78

L

#3 &I78






)

. )

 

`

 C 3  #

G .

=7GHEK?CD7=@D a   `  X



#5

3 3 

F

 

-5 %

-= % &C C  c







# /

V .
V F . .
. .
0. H8

 C$ A78

^

&

U



Z

G

/

h . h . h  8

)

&'

*1)-E


#

&

M/G0I/




#

0 C$%   3 

H3L/

 # -
!f3 % 3 # 

DP

PaD = 


A

T   @CB 0/=)" 

`

MO?_G

MO?_G  h   T  c ( 875% %&)" & ' !#%+#" =7GH EK+?CD7=@D a!EKN EK $LTEK$ ?CD   `M ' 



^

U X

Z

ZeP Y

 # ?7  #  @G P P$-78`$

& ,




#

P

 T   @CB 'e 8%"]& $ U  X

U  X Dh  h .h  h  T ?   M P,EK D>' f '   d  " ,46P,)E % D !  (MOD  " "MO&` E  f %D   =7%GH+#%EK?CD "=@D7 a $ EKN EKEKLTDCEK