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50 51 52</head> 53<body> 54 <div class="wrapper frame"> 55 <!--Sidebar --> 56 <div class="sidebar bit-25"> 57 <a href="http://www.staff.science.uu.nl/~hooft101/"><img class="bigAvatar" src="Images/gerardth.JPG"/></a> 58 <a class="logoLink" href="http://www.staff.science.uu.nl/~hooft101/"><h1 class="logoTitle">Gerard 't Hooft</h1></a> 59 <p class="desc"><!--{Description}--></p> 60 61 62 <div class="splitter"></div> 63 64 65 66 <li class="mainNav"><a class="navLinks" href="languages.html">Languages</a></li> 67 <li class="archive mainNav"><a class="navLinks" href="primarymathematics.html">Primary Mathematics</a></li> 68 <li class="mainNav ask"><a class="navLinks" href="classmech.html">Classical Mechanics</a></li> 69 <li class="mainNav submit"><a class="navLinks" href="optics.html">Optics</a></li> 70 <li class="mainNav submit"><a class="navLinks" href="statmech.html">Statistical Mechanics & Thermodynamics</a></li> 71 <li class="mainNav submit"><a class="navLinks" href="electronics.html">Electronics</a></li> 72 <li class="mainNav submit"><a class="navLinks" href="em.html">Electromagnetism</a></li> 73 <li class="mainNav submit"><a class="navLinks" href="compphys.html">Computational Physics</a></li> 74 <li class="mainNav submit"><a class="navLinks" href="qmech.html">Quantum Mechanics (Non-relativistic)</a></li> 75 <li class="mainNav submit"><a class="navLinks" href="atoms&molecules.html">Atoms & Molecules</a></li> 76 <li class="mainNav submit"><a class="navLinks" href="solidstatephys.html">Solid State Physics</a></li> 77 <li class="mainNav submit"><a class="navLinks" href="nuclearphys.html">Nuclear Physics</a></li> 78 <li class="mainNav submit"><a class="navLinks" href="plasmaphys.html">Plasma Physics</a></li> 79 <li class="mainNav submit"><a class="navLinks" href="advmath.html">Advanced Mathematics</a></li> 80 <li class="mainNav submit"><a class="navLinks" href="specialrel.html">Special Relativity</a></li> 81 <li class="mainNav submit"><a class="navLinks" href="aqmech.html">Advanced Quantum Mechanics</a></li> 82 <li class="mainNav submit"><a class="navLinks" href="pheno.html">Phenomenology</a></li> 83 <li class="mainNav submit"><a class="navLinks" href="gr.html">General Relativity</a></li> 84 <li class="mainNav submit"><a class="navLinks" href="cosmology.html">Cosmology</a></li> 85 <li class="mainNav submit"><a class="navLinks" href="astro.html">Astro-Physics & Astronomy</a></li> 86 <li class="mainNav submit"><a class="navLinks" href="qft.html">Quantum Field Theory</a></li> 87 <li class="mainNav submit"><a class="navLinks" href="susysugra.html">Supersymmetry & Supergravity</a></li> 88 <li class="mainNav submit"><a class="navLinks" href="astroparticles.html">Astro Particle Physics</a></li> 89 <li class="mainNav submit"><a class="navLinks" href="superstrings.html">Super String Theory</a></li> 90 <li class="mainNav submit"><a class="navLinks" href="texts&resources.html">Texts & Other resources</a></li> 91 <li class="mainNav submit"><a class="navLinks" href="responses&questions.html">Responses & Questions</a></li> 92 <li class="mainNav submit"><a class="navLinks" href="acknowledgements.html">Acknowledgements</a></li> 93 94 95 96 97 98 99 <div class="splitter"></div> 100 101 102 </div> 103 104 <!--Content --> 105 <div class="posts bit-75"> 106 107 <div class="post text"> 108 109 <h1 class="postTitle"><a class="postLink" href="index.html">How to become a<br>GOOD Theoretical Physicist</a></h1> 110 <h4 class="timestamp"><a href="{Permalink}" class="timeLink"><!--{TimeAgo}--></a></h4> 111 112 113<style> 114 .top-one { 115 margin-top: 1cm; 116 text-align: justify 117 } 118</style> 119 120 <div class="splitter"></div> 121 122 <h2><p class="top-one"><center><b>Primary Mathematics</b></center></p></h2> 123 124 125 126 <p align="justify">Now, first things first. Are you comfortable with numbers, adding, 127 subtracting, square roots, etc.?</p> 128<ul> 129<li>Natural numbers: 1, 2, 3, â¦</li> 130<li>Integers: â¦, -3, -2, -1, 0, 1, 2, â¦</li> 131<li>
131Rational numbers (fractions): $\dfrac{1}{2}$, $\dfrac{1}{4}$, $\dfrac{3}{4}$, $\dfrac{23791}{773}$, $\dots$</li> 132<li>Real numbers: Sqrt(2) = 1.4142135⦠, Ï = 3.14159265⦠, e = 2.7182818â¦, â¦</li> 133<li>Complex numbers: 2+3i, e<sup>ia</sup>= cos(a) + i sin( a), ⦠they are very important!</li> 134<li>Set theory: open sets, compact spaces. Topology.You may be surprised to learn that they do play a role indeed in physics!</li> 135<li>Algebraic equations. Approximation techniques. Series expansions: the Taylor series. </li> 136<li>Solving equations with complex numbers. Trigonometry: sin(2x)=2sin x cos x, etc.</li> 137<li>Infinitesimals. Differentiation. Differentiate basic functions (sin, cos, exp). </li> 138<li>Integration. Integrate basic functions, when possible. Differential equations. Linear equations.</li> 139<li>The Fourier transformation. The use of complex numbers. Convergence of series.</li> 140<li>The complex plane. Cauchy theorems and contour integration (now this is fun).</li> 141<li>The Gamma function (enjoy studying its properties). </li> 142<li>Gaussian integrals. Probability theory.</li> 143<li>Partial differential equations. Dirichlet and Neumann boundary conditions.</li> 144</ul> 145 146<br> 147<br> 148 <p align="justify">This is for starters. Some of these topics actually come as entire lecture 149 courses. Much of those are essential ingredients of theories in Physics. 150 You donât have to finish it all before beginning with what follows next, 151 but remember to return to those subjects skipped during the first round.</p> 152 153 154 <div class="splitter"></div> 155 156<ul> 157<li><a href="http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/">Beginning Algebra</a></li> 158<li><a href="http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/index.htm">Intermediate Algebra</a></li> 159<li><a href="http://www.clarku.edu/~djoyce/trig/">Dave E. Joyce's Trigonometry course</a></li> 160<li><a href="http://www-thphys.physics.ox.ac.uk/users/JamesBinney/complex.pdf">Prof. James Binney's course on Complex Numbers (*.pdf)</a></li> 161<li><a href="http://www.msc.uky.edu/ken/ma109/notes.htm">(Nearly) Complete overview of Primary Mathematics (K. Kubota, Kentucky)</a></li> 162<li>Chris Pope's lecture notes: <a href="http://faculty.physics.tamu.edu/pope/mch1.ps">Methods 1</a> 163 <a href="http://faculty.physics.tamu.edu/pope/mch2.ps">Methods 2</a></li> 164<li><a href="http://people.math.gatech.edu/~cain/winter99/complex.html">The complex plane, Cauchy theorems and contour integration.</a></li> 165</ul> 166 167 168 </div> 169 170 171 <div id="disqus_thread"></div> 172
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