Question Number 1486 by 112358 last updated on 13/Aug/15
$$\mathrm{While}\:\mathrm{this}\:\mathrm{may}\:\mathrm{be}\:\mathrm{a}\:\mathrm{bit}\:\mathrm{off}\: \\ $$$$\mathrm{the}\:\mathrm{usual}\:\mathrm{Q}\:\mathrm{n}\:\mathrm{A}\:\mathrm{posts}\:\mathrm{here}, \\ $$$$\mathrm{what}\:\mathrm{advice}\:\mathrm{can}\:\mathrm{be}\:\mathrm{given}\:\mathrm{to}\: \\ $$$$\mathrm{someone}\:\mathrm{wishing}\:\mathrm{to}\:\mathrm{successfully} \\ $$$$\mathrm{carry}\:\mathrm{out}\:\mathrm{undergraduate}\:\mathrm{studies} \\ $$$$\mathrm{in}\:\mathrm{mathematics}?\:\mathrm{I}'\mathrm{m}\:\mathrm{worried}\: \\ $$$$\mathrm{about}\:\mathrm{my}\:\mathrm{problem}\:\mathrm{solving}\:\mathrm{skills} \\ $$$$\mathrm{and}\:\mathrm{my}\:\mathrm{ability}\:\mathrm{to}\:\mathrm{consider}\:\mathrm{all} \\ $$$$\mathrm{aspects}\:\mathrm{of}\:\mathrm{a}\:\mathrm{problem}.\: \\ $$$$ \\ $$
Answered by 2closedStringsMeet last updated on 16/Aug/15
$${Considering}\:{all}\:{aspects}\:{of}\:{a}\:{problem} \\ $$$${shouldnt}\:{be}\:{your}\:{biggest}\:{concern};\: \\ $$$${Instead}\:{yearn}\:{to}\:{well}\:{focus}\:{on}\:{the}\: \\ $$$${underlying}\:{assumptions}\:{that}\:{given} \\ $$$${problems}\:{seem}\:{to}\:{imply};\:{and}\:{solve}\:{from} \\ $$$${a}\:{thereof}\:{connection}\:.\:{Quite}\:{simple} \\ $$$${story}−{telling};\:{once}\:{you}\:{know}\:{the}\: \\ $$$${grammar},\:{you}\:{tell}\:{it}\:{by}\:{finding} \\ $$$${ways}\:{to}\:{suitingly}\:{connect}\:{given}\:{events}; \\ $$$${and}\:{not}\:{by}\:{intending}\:{to}\:{consider}\:{all} \\ $$$${possible}\:{ways}\:{to}\:{connect}\:{them}. \\ $$$${As}\:{a}\:{theoretical}\:{physics}\:{student}, \\ $$$${mathematics}\:{has}\:{become}\:{a}\:{language} \\ $$$${for}\:{me};\:{once}\:{had}\:{it}\:{been}\:{a}\:{simple}\:{tool}.\: \\ $$$${Problem}\:{solving}\:{skills}\:{come}\:{to}\:{me} \\ $$$${not}\:{by}\:{thinking}\:{about}\:{the}\:{problem}\:{itself}, \\ $$$${but}\:{by}\:{letting}\:{the}\:{assumptions}\:{of}\:{the} \\ $$$${problem}\:{be}\:{true},\:{and}\:{so},\:{investigate} \\ $$$${its}\:{implications}. \\ $$$${Suggesting}\:{that}\:{you}\:{solve}\:{a}\:{bunch}\:{of} \\ $$$${problems},\:{i}\:{thought},\:{wouldnt}\:{hit}\:{the}\:{spot}. \\ $$$${In}\:{my}\:{experience}\:{with}\:{mathematics}, \\ $$$${in}\:{general},\:{is}\:{the}\:{power}\:{of}\:{assumption} \\ $$$${that}\:{lets}\:{you}\:{discover}\:{new}\:{ways}\:{to}\:{see} \\ $$$${a}\:{problem};\:{thereof}\:{coming}\:{close}\:{to} \\ $$$${seeing}\:''{all}''\:{aspects}\:{of}\:{such}\:{problem}. \\ $$$${For}\:{a}\:{mathematics}\:{carrier}\:{in}\:{general}, \\ $$$${i}\:{would}\:{advice}\:{you}\:{to}\:{talk}\:{to}\:{as}\:{many} \\ $$$${mathematicians}\:{as}\:{you}\:{can};\:{the}\:{push} \\ $$$${lies}\:{in}\:{the}\:{interest}\:{and}\:\:{yearn}\:{for}\: \\ $$$${the}\:{mysterious}\:{and}\:{abstract};\:{where} \\ $$$${skills}\:{are}\:{grown}\:{out}\:{of}\:{lust}\:{for}\:{the} \\ $$$${unknown}. \\ $$$$ \\ $$
Commented by userid1 last updated on 17/Sep/16
$$\mathrm{nice}. \\ $$