In[1]:=8.1+2.5
Out[1]:=10.6

In[2]:=8.1-2.5
Out[2]:=5.6

In[3]:=8.1*2.5
Out[3]:=20.25

In[4]:=8.1/2.5
Out[4]:=3.24

In[5]:=2.5^2
Out[5]:=6.25

In[6]:=%/2
Out[6]:=3.125

In[7]:=%4*2
Out[7]:=6.48

In[8]:=305/177
Out[8]:=305/177

In[9]:=1/6+305/177
Out[9]:=223/118

In[10]:=N[%]
Out[10]:=1.8898305084745763

In[12]:=N[Sqrt[2],50]
Out[12]:=1.4142135623730950488016887242096980785696718753769

In[13]:=Mod[17,3]
Out[13]:=2

In[14]:=Quotient[17, 3]
Out[14]:=5

In[15]:=Round[2.3]
Out[15]:=2

In[16]:=Round[{1.0,1.2,1.4,1.5,1.6,1.8,2.0}]
Out[16]:={1, 1, 1, 2, 2, 2, 2}

In[17]:=Floor[{1.0,1.2,1.4,1.5,1.6,1.8,2.0}]
Out[17]:={1, 1, 1, 1, 1, 1, 2}

In[18]:=Abs[{-1.2,0,3.4}]
Out[18]:={1.2, 0, 3.4}

In[19]:=Abs[3.0+4.0I]
Out[19]:=5.0

In[20]:=Max[23,-32,45,98,17]
Out[20]:=98

In[21]:=Min[23,-32,45,98,17]
Out[21]:=-32

In[22]:=BaseForm[100,2]
Out[22]:=2^^1100100

In[23]:=BaseForm[1000000,16]
Out[23]:=16^^f4240

In[24]:=16^^f4240
Out[24]:=1000000

In[25]:=Divisors[100]
Out[25]:={1, 2, 4, 5, 10, 20, 25, 50, 100}

In[26]:=GCD[24,15]
Out[26]:=3

In[27]:=GCD[20,50,120]
Out[27]:=10

In[28]:=LCM[24,15]
Out[28]:=120

In[29]:=FactorInteger[120]
Out[29]:={{2, 3}, {3, 1}, {5, 1}}

In[30]:=IFactor[120]
Out[30]:=2^3 * 3 * 5

In[31]:=Prime[10]
Out[31]:=29

In[32]:=Table[Prime[i],{i,1,10}]
Out[32]:={2, 3, 5, 7, 11, 13, 17, 19, 23, 29}

In[33]:=PrimePi[30]
Out[33]:=10

In[34]:=PowerMod[2, 3, 7]
Out[34]:=1

In[35]:=PowerMod[3, -1, 7]
Out[35]:=5

In[36]:=Sqrt[2]
Out[36]:=Sqrt[2]

In[37]:=Sqrt[2.0]
Out[37]:=1.4142135623730951

In[38]:=N[Sqrt[2]]
Out[38]:=1.4142135623730951

In[39]:=Sqrt[2.0+3.0I]
Out[39]:=1.6741492280355401 + 0.8959774761298381 I

In[40]:=Sin[Pi/6]
Out[40]:=1/2

In[41]:=Sin[30 Degree]
Out[41]:=1/2

In[42]:=N[Sin[1], 30]
Out[42]:=0.84147098480789650665250232163

In[43]:=Log[1/4, 8]
Out[43]:=-3/2

In[44]:=Log[2, 10]
Out[44]:=Log[2, 10]

In[45]:=Log[2.0, 10.0]
Out[45]:=3.3219280948873626

In[46]:=N[Log[2, 10], 30]
Out[46]:=3.32192809488736234787031942921

In[47]:=Exp[1.0]
Out[47]:=2.718281828459045

In[48]:=N[Pi]
Out[48]:=3.141592653589793

In[49]:=N[E,30]
Out[49]:=2.71828182845904523536028747135

In[50]:=(3x-4y)+(2x-5y)
Out[50]:=5 x - 9 y

In[51]:=(2x)^2+(x2)^2+(yz)^2+(y z)^2
Out[51]:=4 x^2 + x2^2 + yz^2 + y^2 z^2

In[52]:=Expand[(x+2)^2]
Out[52]:=4 + 4 x + x^2

In[7]:=x=a+2b
Out[1]:=a + 2 b

In[3]:=Expand[x^3]
Out[3]:=a^3 + 6 a^2 b + 12 a b^2 + 8 b^3

In[4]:=Clear[x]
Out[1]:=Null

In[2]:=Factor[x^4+x^2+1]
Out[2]:=(1 - x + x^2) (1 + x + x^2)

In[3]:=Factor[x^10-1]
Out[3]:=(-1 + x) (1 + x) (1 - x + x^2 - x^3 + x^4) (1 + x + x^2 + x^3 + x^4)

In[4]:=Apart[1/(x^2-1)]
Out[4]:=-1/2/(1 + x) + 1/2/(-1 + x)

In[5]:=Together[-1/2/(1 + x) + 1/2/(-1 + x)]
Out[5]:=1/(-1 + x^2)

In[6]:=Solve[x^3 - 19*x + 30 == 0, x]
Out[6]:={{x -> 3}, {x -> 2}, {x -> -5}}

In[7]:=x /. %
Out[7]:={3, 2, -5}

In[8]:=Solve[x^3-8==0,x]
Out[8]:={{x -> 2}, {x -> -1 - I Sqrt[3]}, {x -> -1 + I Sqrt[3]}}

In[9]:=Solve[{x+y==1,2 x-7 y==11},{x,y}]
Out[9]:={{x -> 2, y -> -1}}

In[10]:=NSolve[x^2 -3 x-1==0,x]
Out[10]:={{x -> 3.302775637731995}, {x -> -0.3027756377319946}}

In[11]:=FindRoot[x/5==Cos[x], {x, 2}]
Out[11]:={x -> 1.306440008369511}

In[12]:=D[x^n,x]
Out[12]:=n x^(-1 + n)

In[13]:=D[x^2 Sin[x],{x,3}]
Out[13]:=6 Cos[x] - 6 x Sin[x] - x^2 Cos[x]

In[14]:=D[x y Sin[x Sin[y]],x]
Out[14]:=y (x Cos[x Sin[y]] Sin[y] + Sin[x Sin[y]])

In[15]:=Integrate[x^n,x]
Out[15]:=1/(1 + n) x^(1 + n)

In[16]:=Integrate[Sin[x],{x,0,Pi}]
Out[16]:=2

In[17]:=NIntegrate[x^2, {x, 0, 1}]
Out[17]:=0.33333333333333337

In[18]:=NIntegrate[Sqrt[1-x^2], {x, 0, 1}]
Out[18]:=0.7853981633974477

In[19]:=Limit[(x^2-1)/(x^3-1),x->1]
Out[19]:=2/3

In[20]:=Limit[Log[x],x->0]
Out[20]:=-Infinity

In[21]:=Series[Sin[x]/(x^2+4),{x,0,8}]
Out[21]:=1/4 x - 5/48 x^3 + 9/320 x^5 - 571/80640 x^7 + O[x]^9

In[22]:=Normal[%]
Out[22]:=1/4 x - 5/48 x^3 + 9/320 x^5 - 571/80640 x^7

In[23]:=Plot[x (x-5)^2,{x,-1,7}]
Out[23]:=-Graphics-

In[24]:=gr=Plot[{Sin[t],Sin[2t]},{t,0,2Pi}]
Out[24]:=-Graphics-

In[25]:=Plot3D[ x y (x^2-y^2) , { x , -2 , 2 } , { y , -2 , 2 }]
Out[25]:=-Graphics-

In[26]:=ParametricPlot3D [ { u Cos [t] , u Sin [t] , u } , { t , 0.5 Pi , 2.5 Pi } , { u ,-Pi , Pi} ]
Out[26]:=-Graphics-

In[27]:=moji={1,c,f,3,a,b}
Out[27]:={1, c, f, 3, a, b}

In[28]:=Length[moji]
Out[28]:=6

In[29]:=moji[[2]]
Out[29]:=c

In[30]:=First[moji]
Out[30]:=1

In[31]:=Range[10]
Out[31]:={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

In[32]:=Range[10,2,-2]
Out[32]:={10, 8, 6, 4, 2}

In[33]:=z^Range[5]
Out[33]:={z, z^2, z^3, z^4, z^5}

In[34]:=Prime[Range[5]]
Out[34]:={2, 3, 5, 7, 11}

In[35]:=Table[n (n+1),{n,6}]
Out[35]:={2, 6, 12, 20, 30, 42}

In[36]:=Table[n (n+1),{n,2,6,2}]
Out[36]:={6, 20, 42}

In[37]:=Table[i-j,{i,3},{j,4}]
Out[37]:={{0, -1, -2, -3}, {1, 0, -1, -2}, {2, 1, 0, -1}}

In[38]:=Permutations[{a,b,c}]
Out[38]:={{a, b, c}, {b, a, c}, {c, a, b}, {a, c, b}, {b, c, a}, {c, b, a}}

In[39]:=Permutations[{a,a,b,c}]
Out[39]:={{a, a, b, c}, {b, a, a, c}, {a, b, a, c}, {b, a, c, a}, {a, b, c, a}, {c, b, a, a}, {b, c, a, a}, {a, c, b, a}, {c, a, b, a}, {a, a, c, b}, {c, a, a, b}, {a, c, a, b}}

In[40]:=Combinations[{a, b, c, d, e}, 3]
Out[40]:={{a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}, {a, b, e}, {a, c, e}, {b, c, e}, {a, d, e}, {b, d, e}, {c, d, e}}

In[41]:=U=Range[1,10]
Out[41]:={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

In[42]:=X={1,2,4,5,7}
Out[42]:={1, 2, 4, 5, 7}

In[43]:=Y={2,3,4,8}
Out[43]:={2, 3, 4, 8}

In[44]:=Z={4,5,7,9}
Out[44]:={4, 5, 7, 9}

In[45]:=Intersection[X,Y]
Out[45]:={2, 4}

In[46]:=Union[X,Z]
Out[46]:={1, 2, 4, 5, 7, 9}

In[47]:=Complement[U,Y]
Out[47]:={1, 5, 6, 7, 9, 10}

In[48]:=Union[Intersection[X,Y],Complement[U,Z]]
Out[48]:={1, 2, 3, 4, 6, 8, 10}

In[49]:=Do[Print[i^2],{i,4}]
1
4
9
16
Out[49]:=Null

In[50]:=For[i=1,i<=4,i=i+1,Print[i^2]]
1
4
9
16
Out[50]:=Null

In[51]:=f[x_]:=x/2+1/x
Out[51]:=f[x_] := x/2 + 1/x

In[52]:=f[1]
Out[52]:=3/2

In[53]:=f[f[1]]
Out[53]:=17/12

In[54]:=Nest[f,1,3]
Out[54]:=577/408

In[55]:=NestList[f,1,5]
Out[55]:={1, 3/2, 17/12, 577/408, 665857/470832, 886731088897/627013566048}

In[56]:=NestList[f,1.0,5]