<p>Math is very logical and REAL. NOTHING LIKE philosophy.</p>
<p>Then you don't know much about philosophy.</p>
<p>... and if you think intro to calculus is a "very high level" course (such as one UCLAri was referring to), then you also need to look into more about higher level mathematics.</p>
<p>Its the highest math course at my high school. And isn't calculus consider very high level since FEW students take past calc4 in college, not even engineering majors. And calc is not very philosophical at all.</p>
<p>Clearly, people here have no idea about the long and intertwined history of math and philosophy.</p>
<p>Pythagoras, Euclid, Descartes, Spinoza, Bertrand Russell, etc...were all mathematicians AND philosophers. Even people like Pascal and Newton wrote philosophical treatises.</p>
<p>Upper-level math courses are VERY theoretical--consider algebraic topology, for one. Not only that , but many math courses require students to do proofs--something used by philosophers, logicians and mathematicians alike.</p>
<p>Anybody who says that math and philosophy are nothing alike or have nothing in common really has no clue what they are talking about.</p>
<p>Just because few people have a need to go beyond calculus doesn't mean that it is a high level math course... it really isn't.</p>
<p>Is that similar to algebra?? because I've took algebra and its not philosophical. in fact not even calculus, one of the hardest math, is philosophical.</p>
<p>what is this "high-level" math course ur talking about? engineering majors dont take past calc4. and that basically is the limit on which math is useful and can be applied. anything past that is basically useless.</p>
<p>not even calculus, one of the hardest math</p>
<p>did you miss my last post or something? linear algebra, number theory, differential geometry, complex analysis - the list goes on. My roommate is a math major, and all he does is complex proofs and analysis. dude, its obvious you don't know what you're talking about (especially if you think the calculus you're taking now is the highest level math engineers take) - if you want to go learn more about higher math and philosophy in general and then argue intelligently about it, please do - otherwise this discussion goes nowhere.</p>
<p>I think we should ignore "MysticGohan..." He doesn't seem to realize that calculus is only one branch of mathematics. I mean, what does he think math majors take? Cal III+IV and that's it? I suggest that he should check a few colleges' math dept. websites and see just how complex and abstract it can get...</p>
<p>And calculus only becomes high-level math once you get to partial differential equations. So no, overall, I don't consider it to be a high level math.</p>
<p>Oh, by the way--what the hell do you mean when you say that math isn't "philosophical?" Duh, math doesn't debate complex metaphysical and moral issues. But the methods in which both are undertaken are very similar.</p>
<p>We should stop bothering with "MysticGohan..." In another thread, he said that i-banking was a "new" industry and that "there wouldn't be much competition" since nobody in his high school has heard of it. :rolleyes:</p>
<p>lol man, what are they teaching in high schools these days</p>
<p>"what is this "high-level" math course ur talking about? engineering majors dont take past calc4. and that basically is the limit on which math is useful and can be applied. anything past that is basically useless."</p>
<p>Why did you just copy a quote and not add anything yourself?</p>
<p>Well it is true that engineers (not math majors, obviously) don't take past Calc4.. they might take other math courses such as statistics or discrete math. Then again, it all depends on the school's curriculum.</p>
<p>On a side note, can anyone explain to me briefly what you learn in advanced calc1&2 (analysis), algebra1&2.. im looking at my school's course registrar and can't seem to figure it out. Thanks.</p>
<p>DUDE if engineers DONT need past calc4 then anything past calc4 is USELESS and not applicable. Engineers need alot of math, they take the most math besides math majors. That means the only useful math stops at calc4. Studying any thing past that is a failure no matter what grades are achieved.</p>
<p>OK. Ignorance is just a little too much for me. I have taken the liberty of listing most of the courses in the UC Berkeley Math Department catalog and explaining the relevance to most in Engineering. Many of the courses in here seem useless, but often serve as important prerequisite courses for other things. Like 202A and B are both Analysis offer the measure theory etc. for things like the theory of dynamical systems.
Upper Division Courses
C103 -- Introduction to Mathematical Economics [3 units]
Obviously this is related pretty useful </p>
<p>104 -- Introduction to Analysis [4 units]
H104 -- Introduction to Analysis [4 units]
105 -- Second Course in Analysis [4 units]
These two courses are basically theory based Calculus Classes that serve as foundation for higher level courses</p>
<p>110 -- Linear Algebra [4 units]
H110 -- Linear Algebra [4 units]
very basic
113 -- Introduction to Abstract Algebra [4 units]
H113 -- Introduction to Abstract Algebra [4 units]<br>
114 -- Second Course in Abstract Algebra [4 units]
Quantum Mechanics, actually most classical mechanics courses use a whole lot of Algebra: Groups, Rings, Fields, Modules.</p>
<p>115 -- Introduction to Number Theory [4 units]
Cryptography, computer science, image analysis etc.</p>
<p>118 -- Wavelets and Signal Processing [4 units]
Pretty self explanatory</p>
<p>119 -- Introduction to Applied Mathematics [4 units]
Also pretty explanatory</p>
<p>121A -- Mathematical Tools for the Physical Sciences [4 units] </p>
<p>Same</p>
<p>121B -- Mathematical Tools for the Physical Sciences [4 units] </p>
<p>Same</p>
<p>123 -- Ordinary Differential Equations [4 units]
If you don't know these and PDEs, then you don't deserve to do any kind of science.</p>
<p>125A -- Mathematical Logic [4 units]
One of the only less useful for engineering</p>
<p>126 -- Introduction to Partial Differential Equations [4 units]
see previous on ODEs</p>
<p>127 -- Mathematical and Computational Methods in Molecular Biology [4 units]
Duh </p>
<p>128A -- Numerical Analysis [4 units]
Duh </p>
<p>128B -- Numerical Analysis [4 units]
Duh</p>
<p>130 -- The Classical Geometries [4 units]
Not too useful</p>
<p>135 -- Introduction to the Theory of Sets [4 units]
Not too useful either. </p>
<p>140 -- Metric Differential Geometry [4 units]
This is pretty damn useful if you ever want to do calculus on manifolds. And since if you ever want to learn classical mechanics, you pretty much have to do this.</p>
<p>141 -- Elementary Differential Topology [4 units]
Huge applications in Physics. Quantum Field Theory which has proved very useful in Condensed matter physics and many other fields. Dynamical Systems</p>
<p>142 -- Elementary Algebraic Topology [4 units]
less useful, but hey, if you don't know this then you can't do much of the extra stuff. see the graduate one</p>
<p>160 -- History of Mathematics [4 units]
can't say much for this</p>
<p>170 -- Mathematical Methods for Optimization [4 units]
Calculus of Variations is a must for engineers</p>
<p>172 -- Combinatorics [4 units]
Huge, huge applications in computer science</p>
<p>185 -- Introduction to Complex Analysis [4 units]
H185 -- Introduction to Complex Analysis [4 units]
complex numbers might seem useless, but they aren't. This is definelty a foundational course for engineers. Quote from wikipedia "Traditionally, complex analysis, in particular the theory of conformal mappings, has many applications in engineering"</p>
<p>189 -- Mathematical Methods in Classical and Quantum Mechanics [4 units] </p>
<p>Duh</p>
<p>Graduate Courses
202A -- Introduction to Topology and Analysis [4 units]
You learn about topology and analysis, which leads up to the next few courses.</p>
<p>202B -- Introduction to Topology and Analysis [4 units] </p>
<p>204A -- Ordinary and Partial Differential Equations [4 units]
Duh Again</p>
<p>204B -- Ordinary and Partial Differential Equations [4 units]
And again </p>
<p>205 -- Theory of Functions of a Complex Variable [4 units]
And Again</p>
<p>206 -- Banach Algebras and Spectral Theory [4 units]
Operator Algebras and this kind of stuff plays a huge role in functional analysis. Nuclear Engineering, Quantum Physics, etc. </p>
<p>207 -- Unbounded Operators [4 units]
same as above</p>
<p>208 -- C*-algebras [4 units]
same as above</p>
<p>209 -- Von Neumann Algebras [4 units]
noncommutative version of above</p>
<p>212 -- Several Complex Variables [4 units]
self explanatory</p>
<p>214 -- Differentiable Manifolds [4 units]
Manifolds = Dynamical Systems, chaos theory, catastrophe theory etc. General Theory of Relativity</p>
<p>215A -- Algebraic Topology [4 units]
Characteristic Classes, Fibre Bundles, all of which are huge if you ever want to learn about Quantum Anything. </p>
<p>215B -- Algebraic Topology [4 units] </p>
<p>219 -- Ordinary Differential Equations and Flows [4 units] </p>
<p>Duh Again and again</p>
<p>220 -- Methods of Applied Mathematics [4 units] </p>
<p>duh</p>
<p>221 -- Advanced Matrix Computations [4 units] </p>
<p>Quantum and more</p>
<p>222A -- Partial Differential Equations [4 units]
duh</p>
<p>222B -- Partial Differential Equations [4 units]
duh</p>
<p>224A -- Mathematical Methods for the Physical Sciences [4 units]
duh</p>
<p>224B -- Mathematical Methods for the Physical Sciences [4 units] </p>
<p>duh</p>
<p>225A -- Metamathematics [4 units]
cant say much here</p>
<p>225B -- Metamathematics [4 units]
or here</p>
<p>226A -- Abstract Machines and Languages [4 units]
Compusci</p>
<p>227A -- Theory of Recursive Functions [4 units] </p>
<p>Computer Science</p>
<p>227B -- Theory of Recursive Functions [4 units]
Computer Science</p>
<p>228A -- Numerical Solution of Differential Equations [4 units] </p>
<p>Duh</p>
<p>228B -- Numerical Solution of Differential Equations [4 units] </p>
<p>Duh</p>
<p>229 -- Theory of Models [4 units]
Duh </p>
<p>235A -- Theory of Sets [4 units] </p>
<p>not much</p>
<p>235B -- Theory of Sets [4 units] </p>
<p>not much</p>
<p>240 -- Riemannian Geometry [4 units] </p>
<p>GR, Classical Mechanics Dynamical systems, the list goes on.</p>
<p>241 -- Complex Manifolds [4 units] </p>
<p>Many applicatiosn in theoretical physics. Potential theory etc. etc.</p>
<p>242 -- Symplectic Geometry [4 units] </p>
<p>i dont know too much about this</p>
<p>245A -- General Theory of Algebraic Structures [4 units] </p>
<p>nor about this</p>
<p>249 -- Algebraic Combinatorics [4 units] </p>
<p>Combinatorics as always</p>
<p>250A -- Groups, Rings, and Fields [4 units] </p>
<p>Algebra necessary for many things</p>
<p>250B -- Multilinear Algebra and Further Topics [4 units] </p>
<p>Multilinear Algebra: another way of saying tensor algebra which is basically everywhere in the useful kinds of physics.</p>
<p>251 -- Ring Theory [4 units]
algebra</p>
<p>252 -- Representation Theory [4 units] </p>
<p>253 -- Homological Algebra [4 units] </p>
<p>Good</p>
<p>254A -- Number Theory [4 units] </p>
<p>Duh</p>
<p>254B -- Number Theory [4 units] </p>
<p>Duh</p>
<p>255 -- Algebraic Curves [4 units] </p>
<p>Duh</p>
<p>256A -- Algebraic Geometry [4 units] </p>
<p>256B -- Algebraic Geometry [4 units] </p>
<p>257 -- Group Theory [4 units] </p>
<p>algebra</p>
<p>258 -- Classical Harmonic Analysis [4 units] </p>
<p>duh</p>
<p>261A -- Lie Groups [4 units] </p>
<p>mechanics, Classical and Quantum</p>
<p>261B -- Lie Groups [4 units] </p>
<p>265 -- Differential Topology<br>
Dynamical Systems</p>
<p>Note that these are only the applications to the field of engineering. Almost every single one has many many many many many many many more applications in the field of physics. In fact much of the advanced mathematics grew out of discoveries in physics. Char classes, fiber bundles, algeom etc etc etc</p>
<p>shows how much some people really know about math. Boy, you have only seen the tip of the iceberg</p>
<p>I would like to say I appreciate mruncleramos's undertaking. Even though such a short post doesn't coompare too well:</p>
<p>I would just like to point out that even maybe the 5 "not very applicable ones" really are more applicable then what you think they would be, as they are more as preliminary in order to understand the other applicable things.</p>
<p>Studying math for its own sake is rarely as futile as some make it out to be. Think of it this way, if you found a new natural resource, or material, or whatever, there's always a way to make some sort of use out of it, even if its just the mortar of something larger.</p>
<p>tell me whens the last time you applied 160 -- History of Mathematics [4 units] to whatever job your doing? if its not applicable to YOUR jobs, its useless, futile, and a waste.</p>
<p>Life is too short to make all the mistakes yourself, thats why we learn from history. :) </p>
<p>History is probably more applicable than any engineering course.</p>
<p>You still didn't point to a specific example on YOUR job where you needed to know the history of math. Theres no practical use for it. I'll leave the learning to the historians and people with PhD's. I don't care about learning. How sucessful you are is determined by your salary. And you assume I wanted to learn. When have I ever claimed to be a smart man? Quit accusing me of possessing intelligence.</p>
<p>^^^</p>
<p>Trolling in its finest form...</p>
<p>I'm afraid that's about all MysticGohan is.</p>
<p>Quit accusing me of possessing intelligence.</p>