Jarník attended the First Czech Real Gymnasium, similar to the German Realschule, in Ječná Street in Prague. Jirí Vesely writes :-
We do not know whether Jarník's choice of school was connected with the wish to master modern languages or whether the choice was influenced just by the site of the school, which was located quite close to the place where the Jarníks were living at that time.Whatever his reason for attending this school the education he received there meant that he had problems with entering a university. He graduated from the Real Gymnasium on 7 July 1915, but without having studied Latin. Latin was necessary for admission as a student at the Charles University in Prague where he wished to go to study mathematics and physics. However, he was admitted in 1915 as an extraordinary student, only becoming a properly registered student three semesters later after passing a Latin examination. He received an exemption from military service on 17 January 1917.
At the Charles University, Jarník attended mathematics lectures delivered by Karel Petr (1868-1950), Bohuslav Hostinsky (1884-1951), Karel Rychlík (1885-1968), Jan Sobotka (1862- 1931), Bohumil Bydzovsky (1880-1969) and Václav Láska (1862-1943). He was most influenced by Karel Petr who had moved from Brno to Prague in 1902. Jarník also attended physics lectures by Bohumil Kucera (1874-1921), Václav Posejpal (1874-1935), Vladimír Václav Heinrich (1884-1965) and František Závisška (1879-1945). His university education was broad for, in addition to mathematics and physics, he took courses on philosophy, psychology, chemistry, Czech literature, and German literature. Jarník graduated from the Charles University in 1919.
After graduating, Jarník was appointed as an assistant to Jan Vojtěch (1879-1953) at the Technical University of Brno. Jan Vojtěch, after teaching in secondary schools in Prague, Olomouc, and Brno had taught at the Technical University of Brno from 1916, being appointed as an extraordinary professor on 25 February 1918. His main mathematical interests were on the theory of transformations, the theory of plane curves of the sixth degree and projective geometry. In Brno, Jarník met Matyáš Lerch who influenced his mathematical development. While carrying out his duties in Brno, Jarník continued to work on his doctoral thesis and he submitted On the roots of Bessel functions (Czech) to the Charles University in Prague and, after defending his thesis, was awarded his doctorate in 1921.
After the award of his doctorate, he returned to Prague where he was appointed as an assistant to Karel Petr. As Petr's assistant he worked on analysis and number theory. In particular he studied the number theory works of Edmund Landau. At this time Petr was writing his book Pocet diferenciální (cást analytická) and Jarník helped with proof-reading but also made improvements to the text which Petr acknowledged in the published work. During this period Jarník published On Bolzano's function (Czech) (1922) in which he :-
... proved among other that Bolzano's function is in fact the oldest example of a continuous nowhere differentiable function.In 1923 he went to the University of Göttingen to work with Edmund Landau. Returning to his post in Prague in February 1925, later that year, in December, he moved from his assistant position to that of docent after submitting his habilitation dissertation O mřížový