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maximR	Dec 13 2013, 09:54 PM Return to original view \| Post #21
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(Critical_Fallacy @ Dec 13 2013, 09:46 PM) A very good suggestion. Preparing the tutorial notes in MSWord, convert to picture, resize, touch-up and upload are very inconvenient. Therefore, I second that! As you can see, I typed the following equation using LaTeX commands. e^{i\pi} + 1 = 0 Can anyone identify the most compact equation in all of mathematics? Find out the answer in http://www.codecogs.com/latex/eqneditor.php Yes , an equation which combines i , pi , e , 1 and 0 ! Very beautiful equation . I would appreciate it if you could provide tutorials on Logic . https://fbcdn-sphotos-h-a.akamaihd.net/hpho...650586348_n.jpg The link will bring you to a page of 2013 Further Mathematics STPM Repeat Paper . In Q1 , it asks for the validity of propositions , but in my book , it says that a proposition and an argument are two different things . A proposition can be true or false , valid and invalid are incorrect terms to refer to propositions . I know how to do (a) and (b) , but what about the conclusion ?
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maximR	Dec 13 2013, 09:57 PM Return to original view \| Post #22
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(RED-HAIR-SHANKS @ Dec 13 2013, 09:55 PM) Hmmm I kinda fathom the question, but I have no idea on how to show that it's rational or not. A ver tricky one I'd say.... Try a simpler one then : Proof , or disproof that the product of two irrational numbers results in a rational number .
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maximR	Dec 13 2013, 10:04 PM Return to original view \| Post #23
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(Critical_Fallacy @ Dec 13 2013, 10:01 PM) Can you name that beautiful equation? Hint: See Post #226 on Page 12. Euler's Identity , as Sal Khan of KhanAcademy put it , ' If this doesn't blow your mind , you have no emotion . ' , in his long derivation of this identity . I think it involves some series but I can't recall .
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maximR	Dec 13 2013, 10:15 PM Return to original view \| Post #24
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(Critical_Fallacy @ Dec 13 2013, 10:01 PM) Can you name that beautiful equation? Hint: See Post #226 on Page 12. Wait , I think I see something . Suppose that (√2)^(√2) is irrational . Let (√2)^(√2) = a , where a is an irrational number . Raising the powers of both sides by √2 , we have (√2)^2 = a^(√2) ; a^(√2) = 2 ( a is irrational , √2 is also irrational but 2 is rational ) . Call me a nerd , but this is much more exciting than a lot of things I've seen !
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maximR	Dec 13 2013, 10:17 PM Return to original view \| Post #25
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(v1n0d @ Dec 13 2013, 10:15 PM) The solution makes use of the Gelfond-Schneider theorem. Correct, but what happens when a≠b? Can the working that I've shown be accepted ? It seems a bit simple and doesn't touch on anything about transcendental numbers .
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maximR	Dec 13 2013, 10:18 PM Return to original view \| Post #26
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(v1n0d @ Dec 13 2013, 10:15 PM) The solution makes use of the Gelfond-Schneider theorem. Correct, but what happens when a≠b? Didn't think of that . Is there a general proof ?
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maximR	Dec 13 2013, 10:20 PM Return to original view \| Post #27
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(RED-HAIR-SHANKS @ Dec 13 2013, 10:08 PM) I'm not so sure about this, but I might give it a try. We know that √2 is irrational. But if we multiply √2 with √2: √2 x √2 = 2/1 Hence, 2 in this case, is rational. What about a general proof ?
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maximR	Dec 13 2013, 10:23 PM Return to original view \| Post #28
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(v1n0d @ Dec 13 2013, 10:13 PM) The conclusion is that for every x∈R, ∃ an inverse y∈R ∋x+y∈R. ∋ means 'such that' ? Any reasoning behind this , maybe a more detailed explanation ? I'm sorry , I've a lot to go .
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maximR	Dec 13 2013, 10:32 PM Return to original view \| Post #29
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(v1n0d @ Dec 13 2013, 10:24 PM) It's not necessary to provide general proof. Existence is shown if you can provide just one example where the property holds. Sorry, creature of habit. ∋ means such that. For any real number, an additive inverse exists within the set so that that number added to it's inverse will yield the additive identity, 0. This is a basic property of the vector space R of real numbers. You can find more info on this in books on linear algebra. Can I say : For every x∈R, ∃ an inverse y∈R such that x+y = 0 instead of x+y∈R ?
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maximR	Dec 13 2013, 10:40 PM Return to original view \| Post #30
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(RED-HAIR-SHANKS @ Dec 13 2013, 10:33 PM) Wait, did I miss something? If I were to multiply an irrational number(√2) with itself, then I'll get a rational number, which is 2. So, the product of two irrational numbers is rational. Did I left out anything vital? Try this out : √2*√3 , do you still get a rational number ?
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maximR	Dec 13 2013, 10:59 PM Return to original view \| Post #31
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(v1n0d @ Dec 13 2013, 10:56 PM) The product of irrationals aren't always rational. As with the original question, one only need show an example to prove this statement true. For every x and y such that both are irrational , their product is a rational number . If the statement is revised as above , can one example prove the statement ?
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maximR	Dec 13 2013, 11:02 PM Return to original view \| Post #32
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(v1n0d @ Dec 13 2013, 11:01 PM) You mean disprove. Yes, by providing a counterexample. Okay . Thank you !
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maximR	Dec 15 2013, 09:27 PM Return to original view \| Post #33
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	» Click to show Spoiler - click again to hide... « QUOTE(Krevaki @ Dec 15 2013, 08:13 PM) Posting after a long hiatus: p/s: How's everyone doing? Done with SPM . Starting on more 'advanced' concepts for now to get used to them before PreU . How are the lecturers at USM by the way ? How 'rigorous' is the curriculum for Mech Eng ?
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maximR	Dec 15 2013, 09:35 PM Return to original view \| Post #34
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(v1n0d @ Dec 15 2013, 09:32 PM) USM has brought in plenty of good lecturers due to their apex status. If you're gunning for Mech Eng, I'll suggest UTM as that's their premier course. Most of the other public unis in Malaysia have adopted their syllabus and local reference material was written by lecturers there. They also have strong ties with the industry. If I remember correctly, they signed an MoU so that their Pure Mech degree is recognized by MIT. I'm not into Mechanical Engineering , I'm more geared towards Physics at the moment . This might change , that's why I'm keeping my options open , planning to do A Levels first ( which means IPTA would be out of the picture for me ) , and I've to really dig deep for scholarships after A Levels .
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maximR	Dec 15 2013, 10:03 PM Return to original view \| Post #35
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(v1n0d @ Dec 15 2013, 09:39 PM) When it comes to Physics, my heart is with UM. I spent a couple of days there in the IPO selection camp, it still ranks as one of my top 3 academic experiences. Do you know how I can be involved with the camp ? I've heard of the IMO one but information about IPO is scarce . How do you think I should prepare for it ? IPO involves a lot of college level Physics , not sure if I can manage to self-study everything .
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maximR	Dec 15 2013, 10:09 PM Return to original view \| Post #36
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(Krevaki @ Dec 15 2013, 10:02 PM) I have a secret admirer. » Click to show Spoiler - click again to hide... « Please don't kill me in my sleep. I'm scared. Jokes aside, that is good to know. How were the papers this year? Any "special" things? The lecturers are okay, I guess. But then I have never walked into lectures by lecturers at other universities, unless you count MIT OCW in. The curriculum, by my estimate, would be slightly above the average IPTA standards. There are some courses that are more intense than others, and then there are those that nobody cares about. And let me tell you one fact about engineering: we are very software intensive. So far I've been exposed to 7 different softwares, and there are more to come. By the way, USM accepts A-levels, AUSMAT, SAM and such, other than the usual ones, so IPTA is not entirely out of your reach. (This bit of info may be outdated, so don't quote me on this.) I remember you asking about USM , so yeah , that's how I got to know which course and where you're studying . Yes . A lot . If you've followed the SPM Thread , you will see a lot of rants . The biggest one is Moral , where LPM had to come up with an official reply for many angry parents/students . The sudden change in format , where 'nilai' is no longer needed in essay questions , and 80% comprises of KBKK questions . Sejarah was like this too . I see . I'm still a little bit undecided . I mean I still have a passion for Physics , but interests change , so I'm trying to be exposed to as many things as possible . I'm reading up on Logic , does engineering involve stuff like Mathematical proofs , number theory , etc or does it require only calculus ?
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maximR	Dec 15 2013, 10:15 PM Return to original view \| Post #37
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(v1n0d @ Dec 15 2013, 10:10 PM) Honestly, I have no idea. My F6 physics teacher picked my buddy and I to take the statewide exam and we scored. Next thing you know, we were part of 40-student pool for national team selections. Most of the material covered in the selection camp was college level, so we were pretty lost. I do remember an experiment were asked to approximate the value of g without using a stopwatch. I see . Where are you studying right now , if you don't mind me asking .
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maximR	Dec 15 2013, 10:21 PM Return to original view \| Post #38
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(v1n0d @ Dec 15 2013, 10:17 PM) UTM. UTM offers Mathematics ? I didn't know that . Thanks .
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maximR	Dec 18 2013, 02:49 PM Return to original view \| Post #39
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	» Click to show Spoiler - click again to hide... « QUOTE(Critical_Fallacy @ Dec 18 2013, 10:41 AM) Here is the Applied Physics based ACME network: Aerospace Engineering :: Aerodynamics, Aeroelasticity, Aerothermodynamics, Aerospace Structures, Flight Mechanics, Aircraft Stability & Control, Aircraft Design, Aircraft Fuel Systems, Air-breathing Propulsion, Avionics, Orbital Mechanics, Finite Element Analysis using Abaqus, Computational Fluid Dynamics using ANSYS, 3D CAD Design using CATIA Civil Engineering :: Engineering Mechanics (Statics), Solid Mechanics, Materials Science, Structural Analysis & Design, Soil Mechanics, Fluid Mechanics, Hydraulics, Reinforced Concrete Design, Geotechnical Engineering, Environmental Engineering, Transportation Engineering, Water Resources Engineering, Construction Machinery, Computer-Aided Engineering Design using AutoCAD Mechanical Engineering :: Engineering Mechanics (Statics & Dynamics), Mechanics of Materials, Materials Science, Thermodynamics, Tribology, Design of Machine Elements, Manufacturing Technology, Piston Machines, Pressure Vessels, Heat Exchangers, Turbomachinery, Computer-Aided Engineering Design using AutoCAD & Solidworks Electrical Engineering :: RLC Circuits, AC Circuits, Filter Circuits, Three-Phase Circuits, Logic Circuits, Diodes, Transistors, Operational Amplifiers, Magnetic Circuits & Transformers, Applied Electromagnetics, DC Motors, AC Motors, Signal Processing, Communication Systems, Power Systems, Microelectronics, Intelligent Control Systems, Modeling, Simulation, Analysis, Design & Optimization of Systems using MATLAB & Simulink Thank you . However , I cannot decide based on the topics given . I need to get to the heart and meat of the topic , the contents . As of yet I'm still leaning towards theoretical aspect of Physics . I just bought a First Term Physics STPM book , and I have two volumes of the older version books . Instead of lying to myself that I like a course without even knowing about it ( which many of my friends do ) , I will tell you how I 'feel' about topics in a certain syllabus , I will use STPM Physics' syllabus because I have the books . I believe that this is a sure-fire way of demonstrating my passion towards a subject because I've seen and read the actual contents of the topics , instead of bluffing you that I love Petroleum Engineering ( I am not interested in pipes , not interested in economical ways to transport gases and fluids , not interested in developing new methods or compounds that can sustain the Oil and Gas industry , etc ) . Here you go : I like the 'sureness' of mechanics , I like the idea that the universe behaves in those elegant set of rules ( but I have come to terms with the fact that Newtonian mechanics are just approximations ) . I like Gravitation . I like the study of states of matter ( like force between molecules , etc ) . In the Kinetic Theory of Gases , I like the derivation of the density and pressure of a gas using simple concepts in Newtonian mechanics , the speed of molecules of different gases , and the degrees of freedom of molecules . In Thermodynamics , the molecular explanation of the process of conduction caught my eye . In Second Term , for unknown reasons this part : https://keterehsky.wordpress.com/2011/06/24...etic-induction/ makes me excited on a metaphysical level . The fact that trigonometric functions are used in the study of a.c is also interesting . But what really turns me on is Third Term Physics STPM , Waves and Modern Physics . Geometrical Optics is kind of bland for me , but I like Wave Optics . I really , really like the Atomic Structure sub-topic , everything about Bohr's Postulates are highly intriguing , simply because some assumptions are radical and some parts still use Newtonian mechanics , when I first learned it , I was blown away how I could follow the derivations for the energy levels of a hydrogen atom ( I watched Donald Sadoway's Solid State Chemistry videos for this , Donald Sadoway is an amazing teacher ) . The representation of electromagnetic spectra using different series in Maths is still beyond me but they excite me ( instead of things like our Constitution which really bores me ) . I like everything about X-Ray and Elementary Particles in STPM Physics ( although I feel they are quite short and less emphasised ) . So there you go . This post has been edited by maximR: Dec 18 2013, 02:56 PM
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maximR	Dec 18 2013, 07:39 PM Return to original view \| Post #40
Remember who you are Senior Member 3,864 posts Joined: Dec 2009	QUOTE(iAdor3 Naz @ Dec 18 2013, 07:32 PM) Oh wait.. so in this thread we can ask anything involving maths huh?.. particularly for me calculus.. excited ^^ does anyone have any link to study for chapter 16. Vector Calculus ? .. i can't understand the book explanation Are you books in Korean ?
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