how do i learn compulsory mathematics problems easily?
Answers
This question can be answered in very different ways depending where you are in your fun journey of mathematics.However I will point you to the obvious approaches you could take.
If you are still in college or even in high school,you learn mathematics by exposing yourself to more mathematics. You must however be mindful of two things in this stage,the first is if you are stuck between widening your knowledge of mathematics or going deeper in a specific subject,choose going deeper, or to rephrase my statement,for every class that widens your knowledge or exposes you to other areas of mathematics,choose two classes that goes deeper into the previous material. A good example would be if you completed the equivalent of calculus in U.S universities and wish to decide between taking an analysis course and an introduction to linear algebra course choose the analysis course. The reason I’m advocating this approach is once you have a firm understanding of one area of mathematics,the other area can be tackled easier than if you had a basic understanding. Also if you are stuck between heavy computational/Mechanical courses that rely on computing an answer and courses that rely on proofs,choose proof heavy courses as those courses are what makes us different from computers and being able to do proofs and coming up with new proofs is much more important than doing derivatives or integrals and such.
If you have taken at least 6–8 courses of math in college ,chances are you know which area of mathematics you are interested in,unfortunately beyond this level you have to start researching into the areas you are interested as well as taking heavier courses to really start learning.The problem in this approach is doing these “researches “ is very hard and tiring if you are not affiliated with a university or a research institute ,so start thinking about getting into one if you are not there yet.
Most important of all,mathematics is a very fun and fulfilling journey.
Mathematics is a subject that you cannot avoid. Some love it but, if we’re being honest, most people hate studying maths. The importance of maths for students has never been greater. STEM subjects are the basis for technologies of tomorrow. Most university courses include some level of maths while almost every profession uses maths in some form on a daily basis.
Answer:
ʜᴇʀᴇ ɪs ʏᴏᴜʀ ᴀɴsᴡᴇʀ ⬇️
Step-by-step explanation:
ᴍᴀᴛʜᴇᴍᴀᴛɪᴄs ɪs ᴀ sᴜʙᴊᴇᴄᴛ ᴛʜᴀᴛ ʏᴏᴜ ᴄᴀɴɴᴏᴛ ᴀᴠᴏɪᴅ. sᴏᴍᴇ ʟᴏᴠᴇ ɪᴛ ʙᴜᴛ, ɪғ ᴡᴇ’ʀᴇ ʙᴇɪɴɢ ʜᴏɴᴇsᴛ, ᴍᴏsᴛ ᴘᴇᴏᴘʟᴇ ʜᴀᴛᴇ sᴛᴜᴅʏɪɴɢ ᴍᴀᴛʜs. ᴛʜᴇ ɪᴍᴘᴏʀᴛᴀɴᴄᴇ ᴏғ ᴍᴀᴛʜs ғᴏʀ sᴛᴜᴅᴇɴᴛs ʜᴀs ɴᴇᴠᴇʀ ʙᴇᴇɴ ɢʀᴇᴀᴛᴇʀ. sᴛᴇᴍ sᴜʙᴊᴇᴄᴛs ᴀʀᴇ ᴛʜᴇ ʙᴀsɪs ғᴏʀ ᴛᴇᴄʜɴᴏʟᴏɢɪᴇs ᴏғ ᴛᴏᴍᴏʀʀᴏᴡ. ᴍᴏsᴛ ᴜɴɪᴠᴇʀsɪᴛʏ ᴄᴏᴜʀsᴇs ɪɴᴄʟᴜᴅᴇ sᴏᴍᴇ ʟᴇᴠᴇʟ ᴏғ ᴍᴀᴛʜs ᴡʜɪʟᴇ ᴀʟᴍᴏsᴛ ᴇᴠᴇʀʏ ᴘʀᴏғᴇssɪᴏɴ ᴜsᴇs ᴍᴀᴛʜs ɪɴ sᴏᴍᴇ ғᴏʀᴍ ᴏɴ ᴀ ᴅᴀɪʟʏ ʙᴀsɪs.
7 ᴛɪᴘs ғᴏʀ ᴍᴀᴛʜs ᴘʀᴏʙʟᴇᴍ sᴏʟᴠɪɴɢ
1. ᴘʀᴀᴄᴛɪᴄᴇ, ᴘʀᴀᴄᴛɪᴄᴇ & ᴍᴏʀᴇ ᴘʀᴀᴄᴛɪᴄᴇ
ɪᴛ ɪs ɪᴍᴘᴏssɪʙʟᴇ ᴛᴏ sᴛᴜᴅʏ ᴍᴀᴛʜs ᴘʀᴏᴘᴇʀʟʏ ʙʏ ᴊᴜsᴛ ʀᴇᴀᴅɪɴɢ ᴀɴᴅ ʟɪsᴛᴇɴɪɴɢ. ᴛᴏ sᴛᴜᴅʏ ᴍᴀᴛʜs ʏᴏᴜ ʜᴀᴠᴇ ᴛᴏ ʀᴏʟʟ ᴜᴘ ʏᴏᴜʀ sʟᴇᴇᴠᴇs ᴀɴᴅ ᴀᴄᴛᴜᴀʟʟʏ sᴏʟᴠᴇ sᴏᴍᴇ ᴘʀᴏʙʟᴇᴍs. ᴛʜᴇ ᴍᴏʀᴇ ʏᴏᴜ ᴘʀᴀᴄᴛɪᴄᴇ ᴀɴsᴡᴇʀɪɴɢ ᴍᴀᴛʜs ᴘʀᴏʙʟᴇᴍs, ᴛʜᴇ ʙᴇᴛᴛᴇʀ. ᴇᴀᴄʜ ᴘʀᴏʙʟᴇᴍ ʜᴀs ɪᴛs ᴏᴡɴ ᴄʜᴀʀᴀᴄᴛᴇʀɪsᴛɪᴄs ᴀɴᴅ ɪᴛ’s ɪᴍᴘᴏʀᴛᴀɴᴛ ᴛᴏ ʜᴀᴠᴇ sᴏʟᴠᴇᴅ ɪᴛ ɪɴ ɴᴜᴍᴇʀᴏᴜs ᴡᴀʏs ʙᴇғᴏʀᴇ ᴛᴀᴄᴋʟɪɴɢ ᴛʜᴇ ᴇxᴀᴍ. ᴛʜᴇʀᴇ ɪs ɴᴏ ᴇsᴄᴀᴘɪɴɢ ᴛʜɪs ʀᴇᴀʟɪᴛʏ, ᴛᴏ ᴅᴏ ᴡᴇʟʟ ɪɴ ᴀ ᴍᴀᴛʜs ᴇxᴀᴍ ʏᴏᴜ ɴᴇᴇᴅ ᴛᴏ ʜᴀᴠᴇ sᴏʟᴠᴇᴅ ᴀ ʟᴏᴛ ᴏғ ᴍᴀᴛʜᴇᴍᴀᴛɪᴄᴀʟ ᴘʀᴏʙʟᴇᴍs ʙᴇғᴏʀᴇʜᴀɴᴅ.
2. ʀᴇᴠɪᴇᴡ ᴇʀʀᴏʀs
➡️ ᴡʜᴇɴ ʏᴏᴜ’ʀᴇ ᴘʀᴀᴄᴛɪsɪɴɢ ᴡɪᴛʜ ᴛʜᴇsᴇ ᴘʀᴏʙʟᴇᴍs, ɪᴛ’s ɪᴍᴘᴏʀᴛᴀɴᴛ ᴛᴏ ᴡᴏʀᴋ ᴛʜʀᴏᴜɢʜ ᴛʜᴇ ᴘʀᴏᴄᴇss ғᴏʀ ᴇᴀᴄʜ sᴏʟᴜᴛɪᴏɴ. ɪғ ʏᴏᴜ ʜᴀᴠᴇ ᴍᴀᴅᴇ ᴀɴʏ ᴍɪsᴛᴀᴋᴇs, ʏᴏᴜ sʜᴏᴜʟᴅ ʀᴇᴠɪᴇᴡ ᴛʜᴇᴍ ᴀɴᴅ ᴜɴᴅᴇʀsᴛᴀɴᴅ ᴡʜᴇʀᴇ ʏᴏᴜʀ ᴘʀᴏʙʟᴇᴍ-sᴏʟᴠɪɴɢ sᴋɪʟʟs ʟᴇᴛ ʏᴏᴜ ᴅᴏᴡɴ. ᴜɴᴅᴇʀsᴛᴀɴᴅɪɴɢ ʜᴏᴡ ʏᴏᴜ ᴀᴘᴘʀᴏᴀᴄʜᴇᴅ ᴛʜᴇ ᴘʀᴏʙʟᴇᴍ ᴀɴᴅ ᴡʜᴇʀᴇ ʏᴏᴜ ᴡᴇɴᴛ ᴡʀᴏɴɢ ɪs ᴀ ɢʀᴇᴀᴛ ᴡᴀʏ ᴏғ ʙᴇᴄᴏᴍɪɴɢ sᴛʀᴏɴɢᴇʀ ᴀɴᴅ ᴀᴠᴏɪᴅɪɴɢ ᴛʜᴇ ᴘʀᴏʙʟᴇᴍs
3. ᴅᴏ ɴᴏᴛ ᴛʀʏ ᴛᴏ ᴍᴇᴍᴏʀɪsᴇ ᴛʜᴇ ᴘʀᴏᴄᴇssᴇs.
ᴛʜɪs ɪs ᴄᴏᴜɴᴛᴇʀ-ᴘʀᴏᴅᴜᴄᴛɪᴠᴇ. ɪᴛ ɪs ᴍᴜᴄʜ ʙᴇᴛᴛᴇʀ ᴀɴᴅ ʀᴇᴡᴀʀᴅɪɴɢ ɪɴ ᴛʜᴇ ʟᴏɴɢ-ʀᴜɴ ᴛᴏ ғᴏᴄᴜs ᴏɴ ᴜɴᴅᴇʀsᴛᴀɴᴅɪɴɢ ᴛʜᴇ ᴘʀᴏᴄᴇss ᴀɴᴅ ʟᴏɢɪᴄ ᴛʜᴀᴛ ɪs ɪɴᴠᴏʟᴠᴇᴅ. ᴛʜɪs ᴡɪʟʟ ʜᴇʟᴘ ʏᴏᴜ ᴜɴᴅᴇʀsᴛᴀɴᴅ ʜᴏᴡ ʏᴏᴜ sʜᴏᴜʟᴅ ᴀᴘᴘʀᴏᴀᴄʜ sᴜᴄʜ ᴘʀᴏʙʟᴇᴍs ɪɴ ᴛʜᴇ ғᴜᴛᴜʀᴇ.
ʀᴇᴍᴇᴍʙᴇʀ ᴛʜᴀᴛ ᴍᴀᴛʜs ɪs ᴀ sᴇǫᴜᴇɴᴛɪᴀʟ sᴜʙᴊᴇᴄᴛ sᴏ ɪᴛ’s ɪᴍᴘᴏʀᴛᴀɴᴛ ᴛᴏ ʜᴀᴠᴇ ᴀ ғɪʀᴍ ᴜɴᴅᴇʀsᴛᴀɴᴅɪɴɢ ᴏғ ᴛʜᴇ ᴋᴇʏ ᴄᴏɴᴄᴇᴘᴛs ᴛʜᴀᴛ ᴜɴᴅᴇʀᴘɪɴ ᴀ ᴍᴀᴛʜᴇᴍᴀᴛɪᴄᴀʟ ᴛᴏᴘɪᴄ ʙᴇғᴏʀᴇ ᴍᴏᴠɪɴɢ ᴏɴ ᴛᴏ ᴡᴏʀᴋ ᴏɴ ᴏᴛʜᴇʀ, ᴍᴏʀᴇ ᴄᴏᴍᴘʟᴇx sᴏʟᴜᴛɪᴏɴs ᴡʜɪᴄʜ ᴀʀᴇ ʙᴀsᴇᴅ ᴏɴ ᴜɴᴅᴇʀsᴛᴀɴᴅɪɴɢ ᴛʜᴇ ʙᴀsɪᴄs.
4 .ᴜɴᴅᴇʀsᴛᴀɴᴅ ʏᴏᴜʀ ᴅᴏᴜʙᴛs
sᴏᴍᴇᴛɪᴍᴇs ʏᴏᴜ ᴄᴀɴ ɢᴇᴛ sᴛᴜᴄᴋ ᴛʀʏɪɴɢ ᴛᴏ sᴏʟᴠᴇ ᴘᴀʀᴛ ᴏғ ᴀ ᴍᴀᴛʜs ᴘʀᴏʙʟᴇᴍ ᴀɴᴅ ғɪɴᴅ ɪᴛ ᴅɪғғɪᴄᴜʟᴛ ᴛᴏ ᴍᴏᴠᴇ ᴏɴ ᴛᴏ ᴛʜᴇ ɴᴇxᴛ sᴛᴀɢᴇ. ɪᴛ’s ᴄᴏᴍᴍᴏɴ ғᴏʀ ᴍᴀɴʏ sᴛᴜᴅᴇɴᴛs ᴛᴏ sᴋɪᴘ ᴛʜɪs ǫᴜᴇsᴛɪᴏɴ ᴀɴᴅ ᴄᴏɴᴛɪɴᴜᴇ ᴏɴ ᴛᴏ ᴛʜᴇ ɴᴇxᴛ. ʏᴏᴜ sʜᴏᴜʟᴅ ᴀᴠᴏɪᴅ ᴅᴏɪɴɢ ᴛʜɪs ᴀɴᴅ ɪɴsᴛᴇᴀᴅ sᴘᴇɴᴅ ᴛɪᴍᴇ ᴛʀʏɪɴɢ ᴛᴏ ᴜɴᴅᴇʀsᴛᴀɴᴅ ᴛʜᴇ ᴘʀᴏᴄᴇss ᴏғ sᴏʟᴠɪɴɢ ᴛʜᴇ ᴘʀᴏʙʟᴇᴍ. ᴏɴᴄᴇ ʏᴏᴜ ʜᴀᴠᴇ ɢʀᴀsᴘᴇᴅ ᴀɴ ᴜɴᴅᴇʀsᴛᴀɴᴅɪɴɢ ᴏғ ᴛʜᴇ ɪɴɪᴛɪᴀʟ ᴘʀᴏʙʟᴇᴍ, ʏᴏᴜ ᴄᴀɴ ᴜsᴇ ᴛʜɪs ᴀs ᴀ sᴛᴇᴘᴘɪɴɢ sᴛᴏɴᴇ ᴛᴏ ᴘʀᴏɢʀᴇss ᴛᴏ ᴛʜᴇ ʀᴇᴍᴀɪɴᴅᴇʀ ᴏғ ᴛʜᴇ ǫᴜᴇsᴛɪᴏɴ.
ʀᴇᴍᴇᴍʙᴇʀ: ᴍᴀᴛʜs ʀᴇǫᴜɪʀᴇs ᴛɪᴍᴇ ᴀɴᴅ ᴘᴀᴛɪᴇɴᴄᴇ ᴛᴏ ᴍᴀsᴛᴇʀ.
ɪᴛ ɪs ᴀ ɢᴏᴏᴅ ɪᴅᴇᴀ ᴛᴏ sᴛᴜᴅʏ ᴡɪᴛʜ ᴀ ғʀɪᴇɴᴅ ᴡʜᴏ ʏᴏᴜ ᴄᴀɴ ᴄᴏɴsᴜʟᴛ ᴡɪᴛʜ ᴀɴᴅ ʙᴏᴜɴᴄᴇ ɪᴅᴇᴀs ᴏғғ ᴡʜᴇɴ ᴛʀʏɪɴɢ ᴛᴏ sᴏʟᴠᴇ ᴄᴏᴍᴘʟᴇx ᴘʀᴏʙʟᴇᴍs.
5. ᴄʀᴇᴀᴛᴇ ᴀ ᴅɪsᴛʀᴀᴄᴛɪᴏɴ ғʀᴇᴇ sᴛᴜᴅʏ ᴇɴᴠɪʀᴏɴᴍᴇɴᴛ
ᴍᴀᴛʜᴇᴍᴀᴛɪᴄs ɪs ᴀ sᴜʙᴊᴇᴄᴛ ᴛʜᴀᴛ ʀᴇǫᴜɪʀᴇs ᴍᴏʀᴇ ᴄᴏɴᴄᴇɴᴛʀᴀᴛɪᴏɴ ᴛʜᴀɴ ᴀɴʏ ᴏᴛʜᴇʀ. ᴀ ᴘʀᴏᴘᴇʀ sᴛᴜᴅʏ ᴇɴᴠɪʀᴏɴᴍᴇɴᴛ ᴀɴᴅ ᴀ ᴅɪsᴛʀᴀᴄᴛɪᴏɴ ғʀᴇᴇ ᴀʀᴇᴀ ᴄᴏᴜʟᴅ ʙᴇ ᴛʜᴇ ᴅᴇᴛᴇʀᴍɪɴɪɴɢ ғᴀᴄᴛᴏʀ ᴡʜᴇɴ sᴏʟᴠɪɴɢ ᴄᴏᴍᴘʟᴇx ᴇǫᴜᴀᴛɪᴏɴs ᴏʀ ᴘʀᴏʙʟᴇᴍs ɪɴ ɢᴇᴏᴍᴇᴛʀʏ, ᴀʟɢᴇʙʀᴀ ᴏʀ ᴛʀɪɢᴏɴᴏᴍᴇᴛʀʏ!
sᴛᴜᴅʏɪɴɢ ᴡɪᴛʜ ᴍᴜsɪᴄ ᴄᴀɴ ʜᴇʟᴘ ᴄʀᴇᴀᴛᴇ ᴀ ʀᴇʟᴀxɪɴɢ ᴀᴛᴍᴏsᴘʜᴇʀᴇ ᴀɴᴅ sᴛɪᴍᴜʟᴀᴛᴇ ᴛʜᴇ ғʟᴏᴡ ᴏғ ɪɴғᴏʀᴍᴀᴛɪᴏɴ. ʜᴀᴠɪɴɢ sᴜɪᴛᴀʙʟᴇ ʙᴀᴄᴋɢʀᴏᴜɴᴅ ᴍᴜsɪᴄ ᴄᴀɴ ғᴏsᴛᴇʀ ᴀɴ ᴇɴᴠɪʀᴏɴᴍᴇɴᴛ ᴏғ ᴍᴀxɪᴍᴜᴍ ᴄᴏɴᴄᴇɴᴛʀᴀᴛɪᴏɴ. ᴏғ ᴄᴏᴜʀsᴇ, ʏᴏᴜ sʜᴏᴜʟᴅ sᴛᴇᴇʀ ᴄʟᴇᴀʀ ᴏғ ᴘɪᴛʙᴜʟʟ ᴀɴᴅ ᴇᴍɪɴᴇᴍ, ɪɴsᴛʀᴜᴍᴇɴᴛᴀʟ ᴍᴜsɪᴄ ɪs ᴛʜᴇ ʙᴇsᴛ ᴛʜɪɴɢ ɪɴ ᴛʜᴇsᴇ ᴛɪᴍᴇs.
6. ᴄʀᴇᴀᴛᴇ ᴀ ᴍᴀᴛʜᴇᴍᴀᴛɪᴄᴀʟ ᴅɪᴄᴛɪᴏɴᴀʀʏ
ᴍᴀᴛʜᴇᴍᴀᴛɪᴄs ʜᴀs sᴘᴇᴄɪғɪᴄ ᴛᴇʀᴍɪɴᴏʟᴏɢʏ ᴡɪᴛʜ ᴀ ʟᴏᴛ ᴏғ ᴠᴏᴄᴀʙᴜʟᴀʀʏ ᴡɪᴛʜ ᴀʟʟ ᴛʜᴇ ᴄᴏɴᴄᴇᴘᴛs, ᴛᴇʀᴍɪɴᴏʟᴏɢʏ ᴀɴᴅ ᴅᴇғɪɴɪᴛɪᴏɴs ʏᴏᴜ ɴᴇᴇᴅ ᴛᴏ ᴋɴᴏᴡ. ʏᴏᴜ sʜᴏᴜʟᴅ ɪɴᴄʟᴜᴅᴇ ᴛʜᴇɪʀ ᴍᴇᴀɴɪɴɢs, sᴏᴍᴇ ᴋᴇʏ ᴘᴏɪɴᴛs ᴀɴᴅ ᴇᴠᴇɴ sᴏᴍᴇ sᴀᴍᴘʟᴇ ᴀɴsᴡᴇʀs sᴏ ʏᴏᴜ ᴄᴀɴ ᴄᴏɴsᴜʟᴛ ᴛʜᴇᴍ ᴀᴛ ᴀɴʏ ᴛɪᴍᴇ ᴀɴᴅ ʀᴇᴄᴀᴘ.
7. ᴀᴘᴘʟʏ ᴍᴀᴛʜs ᴛᴏ ʀᴇᴀʟ ᴡᴏʀʟᴅ ᴘʀᴏʙʟᴇᴍs
ᴀs ᴍᴜᴄʜ ᴀs ᴘᴏssɪʙʟᴇ, ᴛʀʏ ᴛᴏ ᴀᴘᴘʟʏ ʀᴇᴀʟ-ᴡᴏʀʟᴅ ᴘʀᴏʙʟᴇᴍs ᴡʜᴇɴ ᴀᴘᴘʀᴏᴀᴄʜɪɴɢ ᴍᴀᴛʜs. ᴍᴀᴛʜs ᴄᴀɴ ʙᴇ ᴠᴇʀʏ ᴀʙsᴛʀᴀᴄᴛ sᴏᴍᴇᴛɪᴍᴇs sᴏ ʟᴏᴏᴋɪɴɢ ғᴏʀ ᴀ ᴘʀᴀᴄᴛɪᴄᴀʟ ᴀᴘᴘʟɪᴄᴀᴛɪᴏɴ ᴄᴀɴ ʜᴇʟᴘ ᴄʜᴀɴɢᴇ ʏᴏᴜʀ ᴘᴇʀsᴘᴇᴄᴛɪᴠᴇ ᴀɴᴅ ᴀssɪᴍɪʟᴀᴛᴇ ɪᴅᴇᴀs ᴅɪғғᴇʀᴇɴᴛʟʏ.
ᴘʀᴏʙᴀʙɪʟɪᴛʏ, ғᴏʀ ᴇxᴀᴍᴘʟᴇ, ᴄᴀɴ ʙᴇ ᴜsᴇᴅ ɪɴ ᴇᴠᴇʀʏᴅᴀʏ ʟɪғᴇ ᴛᴏ ᴘʀᴇᴅɪᴄᴛ ᴛʜᴇ ᴏᴜᴛᴄᴏᴍᴇ ᴏғ sᴏᴍᴇᴛʜɪɴɢ ʜᴀᴘᴘᴇɴɪɴɢ ᴀɴᴅ ᴅᴇᴛᴇʀᴍɪɴᴇ ᴡʜᴇᴛʜᴇʀ ʏᴏᴜ ᴡᴀɴᴛ ᴛᴏ ᴛᴀᴋᴇ ᴀ ʀɪsᴋ sᴜᴄʜ ᴀs ɪғ ʏᴏᴜ sʜᴏᴜʟᴅ ʙᴜʏ ᴀ ʟᴏᴛᴛᴇʀʏ ᴛɪᴄᴋᴇᴛ ᴏʀ ɢᴀᴍʙʟᴇ.
➡️ ᴏʜ ᴀɴᴅ ᴅᴏɴ’ᴛ ғᴏʀɢᴇᴛ ᴛʜᴀᴛ ɪᴛ’s ᴀʟsᴏ ɪᴍᴘᴏʀᴛᴀɴᴛ ᴛᴏ ʜᴀᴠᴇ ᴄᴏɴғɪᴅᴇɴᴄᴇ ɪɴ ʏᴏᴜʀsᴇʟғ ᴀɴᴅ ғᴀᴄᴇ ᴛʜᴇ ᴇxᴀᴍ ᴋɴᴏᴡɪɴɢ ᴛʜᴀᴛ ʏᴏᴜ ʜᴀᴠᴇ ᴘʀᴇᴘᴀʀᴇᴅ.