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|00000000| 5c 64 6f 63 75 6d 65 6e | 74 63 6c 61 73 73 7b 61 |\documen|tclass{a|
|00000010| 72 74 69 63 6c 65 7d 0d | 25 5c 75 73 65 70 61 63 |rticle}.|%\usepac|
|00000020| 6b 61 67 65 7b 6d 61 74 | 68 74 69 6d 65 7d 0d 5c |kage{mat|htime}.\|
|00000030| 70 61 67 65 73 74 79 6c | 65 7b 65 6d 70 74 79 7d |pagestyl|e{empty}|
|00000040| 0d 5c 62 65 67 69 6e 7b | 64 6f 63 75 6d 65 6e 74 |.\begin{|document|
|00000050| 7d 0d 5c 62 65 67 69 6e | 7b 63 65 6e 74 65 72 7d |}.\begin|{center}|
|00000060| 0d 5c 62 66 5c 4c 61 72 | 67 65 20 53 65 62 61 73 |.\bf\Lar|ge Sebas|
|00000070| 74 69 61 6e 27 73 20 6d | 61 74 68 20 74 65 73 74 |tian's m|ath test|
|00000080| 0d 5c 65 6e 64 7b 63 65 | 6e 74 65 72 7d 0d 54 68 |.\end{ce|nter}.Th|
|00000090| 65 20 64 65 66 61 75 6c | 74 20 6d 61 74 68 20 6d |e defaul|t math m|
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|000000b0| 68 5c 20 69 74 61 6c 69 | 63 24 2e 20 54 68 69 73 |h\ itali|c$. This|
|000000c0| 20 73 68 6f 75 6c 64 20 | 6e 6f 74 20 62 65 0d 63 | should |not be.c|
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|000000f0| 20 69 74 61 6c 69 63 7d | 2e 20 20 20 0d 5c 76 65 | italic}|.   .\ve|
|00000100| 72 62 7c 5c 6d 61 74 68 | 62 66 7c 20 70 72 6f 64 |rb|\math|bf| prod|
|00000110| 75 63 65 73 20 5c 74 65 | 78 74 62 66 7b 62 6f 6c |uces \te|xtbf{bol|
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|00000150| 64 6d 61 74 68 20 24 62 | 6f 6c 64 5c 20 66 61 63 |dmath $b|old\ fac|
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|00000170| 7d 20 6c 65 74 74 65 72 | 73 2c 20 61 6e 64 20 62 |} letter|s, and b|
|00000180| 6f 6c 64 20 66 61 63 65 | 20 47 72 65 65 6b 0d 6c |old face| Greek.l|
|00000190| 65 74 74 65 72 73 20 61 | 6e 64 20 6d 61 74 68 65 |etters a|nd mathe|
|000001a0| 6d 61 74 69 63 61 6c 20 | 73 79 6d 62 6f 6c 73 2c |matical |symbols,|
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|000001c0| 62 6f 6c 64 6d 61 74 68 | 7c 20 63 6f 6d 6d 61 6e |boldmath|| comman|
|000001d0| 64 0d 5c 65 6d 70 68 7b | 62 65 66 6f 72 65 7d 20 |d.\emph{|before} |
|000001e0| 67 6f 69 6e 67 20 69 6e | 74 6f 20 6d 61 74 68 20 |going in|to math |
|000001f0| 6d 6f 64 65 2e 20 20 54 | 68 69 73 20 63 68 61 6e |mode.  T|his chan|
|00000200| 67 65 73 20 74 68 65 20 | 64 65 66 61 75 6c 74 20 |ges the |default |
|00000210| 6d 61 74 68 0d 66 6f 6e | 74 73 20 74 6f 20 62 6f |math.fon|ts to bo|
|00000220| 6c 64 2e 20 47 72 65 65 | 6b 20 69 73 20 61 76 61 |ld. Gree|k is ava|
|00000230| 69 6c 61 62 6c 65 20 69 | 6e 20 75 70 70 65 72 20 |ilable i|n upper |
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|00000260| 5c 47 61 6d 6d 61 2c 20 | 5c 44 65 6c 74 61 20 5c |\Gamma, |\Delta \|
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|000002a0| 61 6c 3a 20 5c 28 20 78 | 20 3d 20 32 5c 70 69 20 |al: \( x| = 2\pi |
|000002b0| 5c 52 69 67 68 74 61 72 | 72 6f 77 20 78 20 5c 73 |\Rightar|row x \s|
|000002c0| 69 6d 65 71 20 36 2e 32 | 38 20 5c 29 5c 5c 0d 6d |imeq 6.2|8 \)\\.m|
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|000002e0| 78 7d 20 3d 20 32 5c 70 | 69 20 5c 52 69 67 68 74 |x} = 2\p|i \Right|
|000002f0| 61 72 72 6f 77 20 78 20 | 5c 73 69 6d 65 71 20 36 |arrow x |\simeq 6|
|00000300| 2e 32 38 20 5c 29 5c 5c | 0d 62 6f 6c 64 6d 61 74 |.28 \)\\|.boldmat|
|00000310| 68 20 7b 5c 62 6f 6c 64 | 6d 61 74 68 20 5c 28 78 |h {\bold|math \(x|
|00000320| 20 3d 20 5c 6d 61 74 68 | 62 66 7b 32 7d 5c 70 69 | = \math|bf{2}\pi|
|00000330| 20 5c 52 69 67 68 74 61 | 72 72 6f 77 20 78 20 0d | \Righta|rrow x .|
|00000340| 20 20 20 20 20 20 20 20 | 20 20 20 5c 73 69 6d 65 |        |   \sime|
|00000350| 71 7b 5c 6d 61 74 68 62 | 66 7b 36 2e 32 38 7d 7d |q{\mathb|f{6.28}}|
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|000003a0| 6c 6c 69 67 72 61 70 68 | 69 63 20 66 6f 6e 74 20 |lligraph|ic font |
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|000003c0| 65 74 74 65 72 73 3b 0d | 74 68 65 73 65 20 61 72 |etters;.|these ar|
|000003d0| 65 20 70 72 6f 64 75 63 | 65 64 20 62 79 20 74 68 |e produc|ed by th|
|000003e0| 65 20 5c 76 65 72 62 7c | 5c 6d 61 74 68 63 61 6c |e \verb||\mathcal|
|000003f0| 7c 20 63 6f 6d 6d 61 6e | 64 3a 5c 28 20 5c 6d 61 || comman|d:\( \ma|
|00000400| 74 68 63 61 6c 7b 41 42 | 43 44 45 7d 20 5c 29 0d |thcal{AB|CDE} \).|
|00000410| 20 0d 0d 5c 62 65 67 69 | 6e 7b 65 71 75 61 74 69 | ..\begi|n{equati|
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|00000430| 72 61 63 7b 31 7d 7b 5c | 73 71 72 74 7b 32 5c 70 |rac{1}{\|sqrt{2\p|
|00000440| 69 7d 7d 0d 20 20 5c 69 | 6e 74 5e 74 5f 30 20 65 |i}}.  \i|nt^t_0 e|
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|00000480| 20 5c 70 72 6f 64 5f 7b | 6a 5c 67 65 71 20 30 7d | \prod_{|j\geq 0}|
|00000490| 0d 20 20 5c 6c 65 66 74 | 28 5c 73 75 6d 5f 7b 6b |.  \left|(\sum_{k|
|000004a0| 5c 67 65 71 20 30 7d 61 | 5f 7b 6a 6b 7d 20 7a 5e |\geq 0}a|_{jk} z^|
|000004b0| 6b 5c 72 69 67 68 74 29 | 20 0d 3d 20 5c 73 75 6d |k\right)| .= \sum|
|000004c0| 5f 7b 6b 5c 67 65 71 20 | 30 7d 20 7a 5e 6e 0d 20 |_{k\geq |0} z^n. |
|000004d0| 20 5c 6c 65 66 74 28 20 | 5c 73 75 6d 5f 7b 7b 6b | \left( |\sum_{{k|
|000004e0| 5f 30 2c 6b 5f 31 2c 5c | 6c 64 6f 74 73 5c 67 65 |_0,k_1,\|ldots\ge|
|000004f0| 71 20 30 7d 0d 20 20 20 | 20 20 20 20 20 20 20 5c |q 0}.   |       \|
|00000500| 61 74 6f 70 7b 6b 5f 30 | 2b 6b 5f 31 2b 5c 6c 64 |atop{k_0|+k_1+\ld|
|00000510| 6f 74 73 3d 6e 7d 20 20 | 20 20 7d 0d 20 20 20 20 |ots=n}  |  }.    |
|00000520| 20 20 20 20 61 7b 5f 30 | 6b 5f 30 7d 61 5f 7b 31 |    a{_0|k_0}a_{1|
|00000530| 6b 5f 31 7d 5c 6c 64 6f | 74 73 20 20 5c 72 69 67 |k_1}\ldo|ts  \rig|
|00000540| 68 74 29 20 0d 5c 65 6e | 64 7b 65 71 75 61 74 69 |ht) .\en|d{equati|
|00000550| 6f 6e 7d 0d 0d 5c 62 65 | 67 69 6e 7b 65 71 75 61 |on}..\be|gin{equa|
|00000560| 74 69 6f 6e 7d 0d 5c 70 | 69 28 6e 29 20 3d 20 5c |tion}.\p|i(n) = \|
|00000570| 73 75 6d 5f 7b 6d 3d 32 | 7d 5e 7b 6e 7d 0d 20 20 |sum_{m=2|}^{n}.  |
|00000580| 5c 6c 65 66 74 5c 6c 66 | 6c 6f 6f 72 20 5c 6c 65 |\left\lf|loor \le|
|00000590| 66 74 28 5c 73 75 6d 5f | 7b 6b 3d 31 7d 5e 7b 6d |ft(\sum_|{k=1}^{m|
|000005a0| 2d 31 7d 0d 20 20 20 20 | 20 20 20 5c 6c 66 6c 6f |-1}.    |   \lflo|
|000005b0| 6f 72 28 6d 2f 6b 29 2f | 5c 6c 63 65 69 6c 20 6d |or(m/k)/|\lceil m|
|000005c0| 2f 6b 5c 72 63 65 69 6c | 20 0d 20 20 20 20 20 20 |/k\rceil| .      |
|000005d0| 20 5c 72 66 6c 6f 6f 72 | 20 5c 72 69 67 68 74 29 | \rfloor| \right)|
|000005e0| 5e 7b 2d 31 7d 0d 20 20 | 5c 72 69 67 68 74 5c 72 |^{-1}.  |\right\r|
|000005f0| 66 6c 6f 6f 72 0d 5c 65 | 6e 64 7b 65 71 75 61 74 |floor.\e|nd{equat|
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|00000670| 20 62 2c 5c 6c 64 6f 74 | 73 2c 62 7d 5e 7b 6c 5c | b,\ldot|s,b}^{l\|
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|00000690| 5c 6d 61 74 68 72 6d 7b | 65 6c 65 6d 65 6e 74 73 |\mathrm{|elements|
|000006a0| 7d 7d 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |}}      |        |
|000006b0| 20 20 20 20 20 5c 7d 0d | 5c 65 6e 64 7b 65 71 75 |     \}.|\end{equ|
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|00000740| 20 2b 5c 70 69 5e 30 20 | 20 20 20 20 20 20 20 20 | +\pi^0 |        |
|00000750| 5c 5c 5b 35 70 74 5d 0d | 5c 72 69 67 68 74 61 72 |\\[5pt].|\rightar|
|00000760| 72 6f 77 20 5c 6b 61 70 | 70 61 5e 2b 20 2b 5c 70 |row \kap|pa^+ +\p|
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|00000780| 20 5c 5c 0d 5c 73 65 61 | 72 72 6f 77 5c 6c 6f 77 | \\.\sea|rrow\low|
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|00000a10| 65 76 65 7b 61 7d 0d 5c | 6d 62 6f 78 7b 20 63 68 |eve{a}.\|mbox{ ch|
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|00000a40| 20 7b 61 7d 0d 5c 6d 62 | 6f 78 7b 20 76 65 63 3d | {a}.\mb|ox{ vec=|
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|00000a70| 0d 5c 65 6e 64 7b 64 69 | 73 70 6c 61 79 6d 61 74 |.\end{di|splaymat|
|00000a80| 68 7d 0d 5c 65 6e 64 7b | 64 6f 63 75 6d 65 6e 74 |h}.\end{|document|
|00000a90| 7d 0d                   |                         |}.      |        |
+--------+-------------------------+-------------------------+--------+--------+