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I SHO‘BA:
Si a li a’lim – ba qa o a aqqiyo ka ola i: xo ijiy aj iba a mahalliy amaliyo
THE IMPORTANCE AND RELEVANCE OF TEACHING APPLIED
MATHEMATICS IN HIGHER EDUCATION
Au ho s: Begimqulo Fozil Khidi o ich 1
A ilia ion: No dic In e na ional Uni e si y , Senio Lec u e , Depa men o
Economics and Business Managemen 1.
DOI: h ps://doi.o g/10.5281/zenodo.17311689
ABSTRACT
This a icle analyzes he challenges in eaching Applied Ma hema ics in highe educa ion
and sugges s ways o o e come hem. The main pu pose o he s udy is o de elop s uden s’
skills in applying heo e ical knowledge o eal-li e si ua ions. The key p oblem iden i ied is
he insu icien unde s anding o he concep o unc ion, which leads o di icul ies in
applying ma hema ical concep s such as de i a i es and in eg als in p ac ice. As a
me hodology, ma hema ical modeling, analysis h ough eal-li e examples, and
obse a ional app oaches we e employed. The indings indica e ha he use o p ac ical
examples and modeling me hods inc eases s uden s’ in e es in he subjec and os e s he
de elopmen o skills necessa y o hei p o essional ca ee s. In conclusion, i is
ecommended o widely implemen p ac ical examples and modeling app oaches in he
eaching p ocess.
Keywo ds: Applied Ma hema ics, ma hema ical modeling, unc ion, educa ion, applica ion.
INTRODUCTION
Applied Ma hema ics p o ides an oppo uni y o connec heo e ical concep s
wi h eal-li e si ua ions. The ele ance o he opic lies in he ac ha oday,
ma hema ical models a e widely used in economics, heal hca e, ecology,
in o ma ion echnologies, and o he ields. Teaching his discipline in highe
educa ion h ough mode n app oaches plays a c ucial ole in de eloping s uden s’
analy ical and c ea i e hinking. The main aim o he esea ch is o imp o e s uden s’
abili y o link heo e ical knowledge wi h p ac ice in he eaching o Applied
Ma hema ics.
METHODOLOGY
The esea ch employs ma hema ical modeling, analysis o eal-li e examples, as
well as obse a ion and compa ison me hods. Du ing he lea ning p ocess, unc ions,
hei de i a i es, and in eg als we e explained in connec ion wi h p ac ical examples.
Mo eo e , he e ec i eness o he discipline was examined h ough s uden
in e iews and obse a ions [1-4].
ANALYSIS
Ma hema ical knowledge is p ima ily abs ac in na u e, whe eas Applied
Ma hema ics ocuses on sol ing p oblems and examples encoun e ed in eal li e. Fo
ins ance, issues ela ed o economic and inancial indica o s, indus ial g ow h,
“RAQAMLI TRANSFORMATSIYA DAVRIDA
PEDAGOGIK TA’LIMNI RIVOJLANTIRISH
ISTIQBOLLARI”
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I SHO‘BA:
Si a li a’lim – ba qa o a aqqiyo ka ola i: xo ijiy aj iba a mahalliy amaliyo
heal hca e, en i onmen al esea ch, hyd ome eo ological da a, ou ism, his o ical
monumen s, human li e, psychology, ana omy, ac o s in luencing in o ma ion
p ocessing in he human b ain, and da a ansmission sys ems a e conside ed.
Th ough such examples, he wide applicabili y o ma hema ics is demons a ed.
The use o mode n in o ma ion echnologies-such as anima ions, g aphical
ma e ials, diag ams, and ables-en iches s uden s’ imagina ion and os e s in e es
in he subjec . While eaching his discipline, s uden s’ a ying le els o p epa edness
we e also aken in o accoun . Pa icula ly in highe educa ion, he ansi ion o a
c edi -based sys em also p esupposes he o ganiza ion o dis ance lea ning. F om
his pe spec i e, he main idea o his a icle is ha wi hou unde s anding wha a
unc ion is, i is di icul o comp ehend why ope a ions on unc ions a e needed o
why de i a i es and in eg als mus be calcula ed. Indeed, all p ocesses and
phenomena can be ep esen ed as unc ions. E en e e yday s a emen s can be
exp essed unc ionally. Fo example, he commonly hea d exp ession,
“I am en imes
iche han you,”
can be w i en in he o m o a unc ion. Many simila examples can
be obse ed in eal li e. A comple e unde s anding o unc ions o ms he ounda ion
o acqui ing specialized knowledge [5-7].
Applied Ma hema ics also in oduces concep s such as demand and supply,
o al cos , o al p o i , ne p o i , ma hema ical modeling, and empi ical cu e i ing.
Any eal-li e p ocess o phenomenon exp essed in ma hema ical e ms is called a
ma hema ical model. In algeb a, unc ions a e o en ea ed as models.
Ma hema ical models allow p edic ions abou possible ou comes o p ocesses. I he
p edic ions a e inaccu a e o i expe imen al esul s do no ma ch model ou comes,
hen he model mus be e ised o abandoned. Any model can be econs uc ed by
inco po a ing new da a. Typically, ma hema ical models ep esen con inuous
p ocesses. Fo ins ance, ma hema ical models exis ha can accu a ely p edic
popula ion g ow h a es.
The algo i hm o cons uc ing a ma hema ical model consis s o six s ages:
1. Selec ing a eal-li e p oblem.
2. Collec ing ele an da a.
3. Analyzing he da a.
4. Cons uc ing he model.
5. Tes ing and e ining he model.
6. Explaining and o ecas ing ou comes.
The analysis shows ha s uden s who mas e he concep o unc ions h ough
p ac ical examples a e be e able o unde s and subsequen ma hema ical
concep s. Fo example, economic models, demand and supply cu es, o al and ne
p o i calcula ions a e widely used in p ac ice. Simila ly, in a chi ec u e and
echnology, concep s such as slope and g adien , when explained h ough eal-li e
examples, signi ican ly inc ease s uden s’ in e es in he subjec .
The applica ion o slope can be obse ed in many a eas o daily li e. Fo example,
in oad cons uc ion, slope pe cen ages such as 2%, 3% and 6% a e used o indica e
he s eepness o a oad when ascending a hill. A 3% slope (3% =3
100) means ha o
e e y 100 me e s o ho izon al dis ance, he oad ises by 3 me e s [5].
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I SHO‘BA:
Si a li a’lim – ba qa o a aqqiyo ka ola i: xo ijiy aj iba a mahalliy amaliyo
In a chi ec u e, he slope o a oo is o g ea impo ance: he s eepe he oo ,
he less snow accumula es on i .When designing wheelchai s, slope is also ca e ully
conside ed. Fo accessibili y, he g adien o a amp should no exceed 1
12.
Fu he mo e, many applica ions on de ices such as iPod, iPhone, and Samsung
sma phones can e alua e whe he slope le els a e co ec ly o inco ec ly se . To
unde s and g adien p ac ically, hold you hand pa allel o he g ound — his
ep esen s a 00 g adien . I you hand is aised a a 450 angle, he g adien
co esponds o 100%; a a 22.50 angle, i equals abou 41%; and a a 3.50 angle, he
g adien is only 6%. This is ano he clea example o how slope is applied in eal li e
[5-9].
Th ough he abo e-men ioned examples and p oblems, we ha e illus a ed
se e al eal-li e applica ions o slope and g adien . Such p ac ical applica ions play a
c ucial ole in p epa ing s uden s o hei u u e p o essional ac i i ies.
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