A lot of 1st year students have trouble understanding vector spaces Is there easy way to explain how learn it?
444463
I don't even know what a vector space is and I'm in highschool, maybe you could dumb it down for them and use pictures, kids like pictures!
127169
When we are trying to understand many things in the real world, like the design of machinery, or electrical systems, or the weather, we end up with many variables. Examining the system in the space of its variables is very useful; that is, one assigns a dimension to each variable, and draws pictures and analyzes the surfaces and shapes in the space of variables. If there are more than 3 variables, which there usually are, one is in a very high dimensional space.\n\nYou could not solve or analyze very many real world problems without using high dimensional analyses, such as geometry, topology, etc.
1093109
Yes in both cases! (although for vector spaces, it depends whether you're allowed to pick which field you're working over.  It's not true for vector spaces over the real numbers, for example)\n\nHere's a hint: think about the smallest group there is that isn't cyclic.\n\nOnce you figure it out for groups, you'll realize the same answer works as a vector space over an appropriate (small!) field.
769412
I also have trouble learning from textbooks.  I have found that in order to study from a textbook--at least for me--the best way is to write down a LOT of information.  Write down every definition, write down every equation given, every fact.  Make sure you write at least one sentence for every paragraph.\n\nComplete all the example equations as well as the practice equations.  Do all the assignments in the back of the chapter--even if your teacher doesn't assign them.  Then go back and answer any of the questions and learning objectives listed at the beginning of the chapter.\n\nBy doing these things, especially if you do them before the class in which you are supposed to be learning them, you may find that you are doing better than your classmates.\n\nGood luck!
518238
I think that what's so tough about math, and why everybody hates it so much, is that it's kind of like "gym class" for the brain.  It's hard at first, even painful if you're not used to it, but the only way for it to get better is to do a bunch of hard, boring exercises until you get used to it.  Just as exercising is hard at first, once you start building up muscles it starts to get easier.  It's almost literally the same way for your brain, except instead of "building up" your brain, you're actually creating new pathways in your brain.  It's like clearing a path through a jungle; it's really hard going at first, but it gets easier each time you go over it.\n\nYou do have to "get it" to begin with, though.  That's where your teachers come in.  If you're not understanding something, get them to help.  That's their job.  You may want to talk to your parents about it, and maybe look into getting a tutor.\n\nGood luck.  Just remember:  The second time is always easier than the first.  The third time is easier than the second.  The fourth time...
509374
1.Read the text, slowly and clear ur concepts in between\n2.Read again briskly, underlining the important points.\n3.Make notes of any extras that u know, or u find hard to remember.\n4.Study's shud have a regular regime, give proper 2 hrs if u're not in high-school, otherwise make it 4 hrs., its important.\nFruits are gained either by regular studies/by mugging up to gain marks, i dont like the latter, bcos its not long time, u have to make a start, sticking on to the method above, gradually u'd increase ur speed of learning, and u'll do more in less time.Good Luck!!!!!\nYa n i forgot the maths-well u do sums, solve problems...start from 2 per day to 100 per day, first clear main concepts, n have a command over elementary mathematics...go further n solve problems, its laborious, but fruitful, u wont need to clear concepts again n again if ur basic is strong.Make it strong now or  never, u shud take anyquestion in the book, and start, try teaching maths to juniors, it really helps.
299247
understand da basic concepts.if u hav difficulty understandin them ,get help frm a tutor o ur skol teacher.then, do practice papers & study da theories a LOT!good luck...
233864
1) mathforum.org/ ~klotz/ Vectors/ vectors.html\n2) chem.salve.edu/ VisualizerTutorial/ Algebra.htm\n3) chortle.ccsu.edu/ VectorLessons/ vectorIndex.html\n4) nhn.ou.edu/ ~walkup/ demonstrations/ WebAssignments/ VectorAlgebra002.htm\n\nPS: Delete the spaces
581534
I have written a math book that explains math in plain English.  It is called Mauk Math.  I teach math and I could not find any math book that I liked so I decided to write my own.  Math does NOT have to be difficult.  It CAM be explained in simple terms and it CAN be easy and even FUN.  I use music to learn certain concepts and help retain it.  I use songs to help break it down and make it easier.  For instance, when I teach how to make negative exponents positive I use Will Smith's song, SWITCH. We play the song in class and sing it.  Because that's how you make a negative exponent positive.... you switch it !  If it is on the top of a fraction... you switch it to the bottom.  If it is on the bottom...you switch it to the top...EASY!  In typical math books, they make it difficult by explaining it like this: a number taken to the -nth power in the denominator can be make positive by rewriting the fraction with the denominator as the numerator taken to the nth power.  Ridiculous...especially for the struggling student.  MAUK MATH uses M.C. Hammer's Hammertime to teach the order of operations.  You always do everything in parentheses first.  If something is outside the parentheses....CAN'T TOUCH THAT na na na na. break it down.  Math can be easy and fun with the right book.... my book.  LOL
895063
Google the word algebra help.  Purple math is great, but there are other sites also.  I am sorry I do not have the names at the moment.
301636
Know the material covered in class, it's really that simple. I've found I remember the most when I try and absorb as much as I can when it is actually being gone over in lecture. Often times for me, this means not taking any notes (typically all that you need to know is covered in your class text) and focusing on understanding the concepts being gone over.
4903
Vector problems involve understanding the concept of having a magnitude and direction.\nVectors are just combinations of certain magnitudes in certain directions\n\nEx: F= 2i + 4j + 3k ( this is a force vector which have 3 components in x,y,z plane)\n\nthe most three important operations on vectors are :\nDOT product :\nF . G = (fx,fy).(gx,gy)= fxgx+fygy \nnote that (F.G) is JUST a number \nwe can also define the dot product as :\nF.G= |f||g|cos(theta) .. where (theta) is the angle between the two vectors\n\nthe other product is the Cross Product\nwhich says that F(X)G= |f||g|sin(theta) n. note that the cross product gives a vector perpendicular to the place of the two vectors which contain F and G\n\nthe thirs important rule is that \n|f|=SquareRootOF(fx^2+fy^2+fz^2)\n\nthese are fundementals!
314857
you should try to learn reading any book about vector analysis.\nSomething about vectors:\nhttp://mathworld.wolfram.com/topics/VectorAlgebra.html
913984
// For any vector work I use structures.  For a 3-D vector define a structure as:\n\ntypedef struct\n{\n double x;\n double y;\n double z;\n} VECTOR;\n\n// Write a simple main to exercise some vector functions\n\nvoid main()\n{\n VECTOR VectorAdd(VECTOR A, VECTOR B);\n double VectorDot(VECTOR A, VECTOR B);\n VECTOR VectorCross(VECTOR A, VECTOR B);\n\n VECTOR a, b, c;\n double d;\n\n a.x = 1.0;\n a.y = 3.0;\na.z = 4.3;\n\n b.x = -2.3;\n b.y = 4.4;\n b.z = 1.1;\n\n c = VectorAdd(a, b);\n\n printf("Added: x: %lf, y: %lf, z: %lf&#92;n", c.x, c.y, c.z);\n\n c = VectorCross(a, b);\n\n printf("Crossed: x: %lf, y: %lf, z: %lf&#92;n", c.x, c.y, c.z);\n\n d = VectorDot(a, b);\n\n printf("Dotted: %lf&#92;n", d);\n\n}\n\nVECTOR VectorAdd(VECTOR A, VECTOR B)\n{\n VECTOR C;\n\n C.x = A.x + B.x;\n C.y = A.y + B.y;\n C.z = A.z + B.z;\n\n return C;\n}\n\nVECTOR VectorDot(VECTOR A, VECTOR B)\n{\n return A.x*B.x + A.y*B.y + A.z*B.z;\n}\n\nVECTOR VectorCross(VECTOR A, VECTOR B)\n{\n VECTOR C;\n\n C.x = A.y*B.z - A.z*B.y;\n C.y = A.z*B.x - A.x*B.z;\n C.z = A.x*B.y - A.y*B.x;\n\n return C;\n}
58236
The best way to study math and is to make sure you understand all the fundamentals. Relate them to things you already understand. \nDo lots of different types of problems to figure out what to don't understand.
757330
I am a former Mathematics Educator.  A number of my former students lowest scores were in mathematics.  I suggest that you "borrow" a copy of your Algebra 1 text from the high school that you attended and take the chapter test at the end of each chapter.  This will allow you to assess where you need to begin work in that subject.  It would behoove you to then "trade" for a geometry text and do the same thing.  The same process would help in most other subject matter that you are weak in.  This ALWAYS improved the scores a great deal for my former students.  Have a GREAT WEEKEND!!\nEds
90574
first make sure you have the basic math skills down, then do problems...do problems and then do more problems...lots of practice can make anything easier...unfortunately there is no way to get around this...